diff --git a/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td b/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td
--- a/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td
+++ b/mlir/include/mlir/Dialect/Arithmetic/IR/ArithmeticOps.td
@@ -10,6 +10,7 @@
 #define ARITHMETIC_OPS
 
 include "mlir/Dialect/Arithmetic/IR/ArithmeticBase.td"
+include "mlir/Dialect/Arithmetic/IR/InferIntRangeInterface.td"
 include "mlir/Interfaces/CastInterfaces.td"
 include "mlir/Interfaces/InferTypeOpInterface.td"
 include "mlir/Interfaces/SideEffectInterfaces.td"
@@ -49,7 +50,8 @@
 
 // Base class for integer binary operations.
 class Arith_IntBinaryOp<string mnemonic, list<Trait> traits = []> :
-    Arith_BinaryOp<mnemonic, traits>,
+    Arith_BinaryOp<mnemonic, traits #
+      [DeclareOpInterfaceMethods<InferIntRangeInterface>]>,
     Arguments<(ins SignlessIntegerLike:$lhs, SignlessIntegerLike:$rhs)>,
     Results<(outs SignlessIntegerLike:$result)>;
 
@@ -87,7 +89,8 @@
 // Cast from an integer type to another integer type.
 class Arith_IToICastOp<string mnemonic, list<Trait> traits = []> :
     Arith_CastOp<mnemonic, SignlessFixedWidthIntegerLike,
-                           SignlessFixedWidthIntegerLike, traits>;
+                           SignlessFixedWidthIntegerLike,
+                           traits # [DeclareOpInterfaceMethods<InferIntRangeInterface>]>;
 // Cast from an integer type to a floating point type.
 class Arith_IToFCastOp<string mnemonic, list<Trait> traits = []> :
     Arith_CastOp<mnemonic, SignlessFixedWidthIntegerLike, FloatLike, traits>;
@@ -104,7 +107,8 @@
 class Arith_CompareOp<string mnemonic, list<Trait> traits = []> :
     Arith_Op<mnemonic, traits # [SameTypeOperands, TypesMatchWith<
     "result type has i1 element type and same shape as operands",
-    "lhs", "result", "::getI1SameShape($_self)">]> {
+    "lhs", "result", "::getI1SameShape($_self)">,
+    DeclareOpInterfaceMethods<InferIntRangeInterface>]> {
   let results = (outs BoolLike:$result);
 
   let assemblyFormat = "$predicate `,` $lhs `,` $rhs attr-dict `:` type($lhs)";
@@ -124,6 +128,7 @@
 def Arith_ConstantOp : Op<Arithmetic_Dialect, "constant",
     [ConstantLike, NoSideEffect,
      DeclareOpInterfaceMethods<OpAsmOpInterface, ["getAsmResultNames"]>,
+     DeclareOpInterfaceMethods<InferIntRangeInterface>,
      TypesMatchWith<
     "result and attribute have the same type",
     "value", "result", "$_self">]> {
@@ -973,7 +978,8 @@
     "signless-integer-like or memref of signless-integer">;
 
 def Arith_IndexCastOp : Arith_CastOp<"index_cast", IndexCastTypeConstraint,
-                                                   IndexCastTypeConstraint> {
+                                                   IndexCastTypeConstraint,
+                                                   [DeclareOpInterfaceMethods<InferIntRangeInterface>]> {
   let summary = "cast between index and integer types";
   let description = [{
     Casts between scalar or vector integers and corresponding 'index' scalar or
@@ -1166,7 +1172,8 @@
 //===----------------------------------------------------------------------===//
 
 def SelectOp : Arith_Op<"select", [
-    AllTypesMatch<["true_value", "false_value", "result"]>
+    AllTypesMatch<["true_value", "false_value", "result"]>,
+    DeclareOpInterfaceMethods<InferIntRangeInterface>,
   ] # ElementwiseMappable.traits> {
   let summary = "select operation";
   let description = [{
@@ -1206,7 +1213,7 @@
   let hasCanonicalizer = 1;
   let hasFolder = 1;
   let hasVerifier = 1;
-  
+
   // FIXME: Switch this to use the declarative assembly format.
   let hasCustomAssemblyFormat = 1;
 }
diff --git a/mlir/lib/Dialect/Arithmetic/IR/CMakeLists.txt b/mlir/lib/Dialect/Arithmetic/IR/CMakeLists.txt
--- a/mlir/lib/Dialect/Arithmetic/IR/CMakeLists.txt
+++ b/mlir/lib/Dialect/Arithmetic/IR/CMakeLists.txt
@@ -6,6 +6,7 @@
   ArithmeticOps.cpp
   ArithmeticDialect.cpp
   InferIntRangeInterface.cpp
+  InferIntRangeInterfaceImpls.cpp
 
   ADDITIONAL_HEADER_DIRS
   ${MLIR_MAIN_INCLUDE_DIR}/mlir/Dialect/Arithmetic
diff --git a/mlir/lib/Dialect/Arithmetic/IR/InferIntRangeInterfaceImpls.cpp b/mlir/lib/Dialect/Arithmetic/IR/InferIntRangeInterfaceImpls.cpp
new file mode 100644
--- /dev/null
+++ b/mlir/lib/Dialect/Arithmetic/IR/InferIntRangeInterfaceImpls.cpp
@@ -0,0 +1,817 @@
+//===- InferIntRangeInterfaceImpls.cpp - Integer range impls for arith -===//
+//
+// 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/Dialect/Arithmetic/IR/Arithmetic.h"
+#include "mlir/Dialect/Arithmetic/IR/InferIntRangeInterface.h"
+#include "mlir/IR/BuiltinAttributes.h"
+#include "mlir/IR/OpDefinition.h"
+#include "mlir/Support/LLVM.h"
+
+#include "llvm/Support/Debug.h"
+
+#define DEBUG_TYPE "int-range-analysis"
+
+using namespace mlir;
+using namespace mlir::arith;
+
+/// Get the bitwidth of the attributes holding constants of type `type`.
+static unsigned int getAttrBitwidth(Type type) {
+  if (type.isIndex())
+    return IndexType::kInternalStorageBitWidth;
+  return type.getIntOrFloatBitWidth();
+}
+
+/// Function that evaluates the result of doing something on arithmetic
+/// constants and returns None on overflow.
+using ConstArithFn =
+    llvm::function_ref<Optional<APInt>(const APInt &, const APInt &)>;
+
+/// A [min, max] pair that can be signed or unsigned
+using IntAttrPair = std::pair<Optional<APInt>, Optional<APInt>>;
+
+/// If both `left` and `right` are defined, return the result of
+/// `op(left.getValue(), right.getValue()`, otherwise, return None.
+static Optional<APInt> compute(ConstArithFn op, const Optional<APInt> &left,
+                               const Optional<APInt> &right) {
+  if (!left || !right)
+    return {};
+  return op(left.getValue(), right.getValue());
+}
+
+/// Compute op(minLeft, minRight) and op(maxLeft, maxRight) if possible,
+/// If either computation overflows, make the result unbounded.
+static IntAttrPair computeBoundsBy(ConstArithFn op,
+                                   const Optional<APInt> &minLeft,
+                                   const Optional<APInt> &minRight,
+                                   const Optional<APInt> &maxLeft,
+                                   const Optional<APInt> &maxRight) {
+  Optional<APInt> min, max;
+  if (minLeft && minRight) {
+    min = compute(op, minLeft, minRight);
+    if (!min)
+      return {{}, {}};
+  }
+  if (maxLeft && maxRight) {
+    max = compute(op, maxLeft, maxRight);
+    if (!max)
+      return {{}, {}};
+  }
+  return {min, max};
+}
+
+/// Compute the minimum and maximum of `(op(l, r) for l in lhs for r in rhs)`,
+/// ignoring unbounded values. Returns (null, null) if `op` overflows.
+static IntAttrPair minMaxBy(ConstArithFn op, ArrayRef<Optional<APInt>> lhs,
+                            ArrayRef<Optional<APInt>> rhs,
+                            bool signedCmp = false) {
+  Optional<APInt> min, max;
+  for (Optional<APInt> left : lhs) {
+    for (Optional<APInt> right : rhs) {
+      if (!left || !right) {
+        // A missing lower or upper bound should be accounted for by the parent
+        // function
+        continue;
+      }
+      Optional<APInt> thisResult = compute(op, left, right);
+      if (!thisResult) {
+        return {{}, {}};
+      }
+      if (min) {
+        min = (signedCmp ? thisResult->slt(*min) : thisResult->ult(*min))
+                  ? thisResult
+                  : min;
+      } else {
+        min = thisResult;
+      }
+
+      if (max) {
+        max = (signedCmp ? thisResult->sgt(*max) : thisResult->ugt(*max))
+                  ? thisResult
+                  : max;
+      } else {
+        max = thisResult;
+      }
+    }
+  }
+  return {min, max};
+}
+
+void arith::ConstantOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  // Return null for non-scalar integer constants
+  auto constAttr = getValue().dyn_cast_or_null<IntegerAttr>();
+  Optional<APInt> value;
+  if (constAttr)
+    value = constAttr.getValue();
+  resultRanges.push_back(IntRangeAttrs::range(value, value));
+}
+
+void arith::AddIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+  ConstArithFn uadd = [](auto &a, auto &b) -> Optional<APInt> {
+    bool overflowed = false;
+    APInt result = a.uadd_ov(b, overflowed);
+    if (overflowed)
+      return {};
+    return result;
+  };
+  ConstArithFn sadd = [](auto &a, auto &b) -> Optional<APInt> {
+    bool overflowed = false;
+    APInt result = a.sadd_ov(b, overflowed);
+    if (overflowed)
+      return {};
+    return result;
+  };
+
+  auto urange =
+      computeBoundsBy(uadd, lhs.umin(), rhs.umin(), lhs.umax(), rhs.umax());
+  auto srange =
+      computeBoundsBy(sadd, lhs.smin(), rhs.smin(), lhs.smax(), rhs.smax());
+  resultRanges.emplace_back(urange, srange);
+}
+
+void arith::SubIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  ConstArithFn usub = [](auto &a, auto &b) -> Optional<APInt> {
+    bool overflowed = false;
+    APInt result = a.usub_ov(b, overflowed);
+    if (overflowed)
+      return {};
+    return result;
+  };
+  ConstArithFn ssub = [](auto &a, auto &b) -> Optional<APInt> {
+    bool overflowed = false;
+    APInt result = a.ssub_ov(b, overflowed);
+    if (overflowed)
+      return {};
+    return result;
+  };
+  auto urange =
+      computeBoundsBy(usub, lhs.umin(), rhs.umax(), lhs.umax(), rhs.umin());
+  auto srange =
+      computeBoundsBy(ssub, lhs.smin(), rhs.smax(), lhs.smax(), rhs.smin());
+  resultRanges.emplace_back(urange, srange);
+}
+
+void arith::MulIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  // Determine what bounds we can impose on signed multiplication.
+  bool noNegatives = (lhs.smin() && rhs.smin() && lhs.smin()->isNonNegative() &&
+                      rhs.smin()->isNonNegative());
+  bool canBoundBelow =
+      (lhs.smin() && rhs.smin() && (noNegatives || (lhs.smax() && rhs.smax())));
+  bool canBoundAbove =
+      (lhs.smax() && rhs.smax() && (noNegatives || (lhs.smin() && rhs.smin())));
+
+  ConstArithFn umul = [](auto &a, auto &b) -> Optional<APInt> {
+    bool overflowed = false;
+    APInt result = a.umul_ov(b, overflowed);
+    if (overflowed)
+      return {};
+    return result;
+  };
+  ConstArithFn smul = [](auto &a, auto &b) -> Optional<APInt> {
+    bool overflowed = false;
+    APInt result = a.smul_ov(b, overflowed);
+    if (overflowed)
+      return {};
+    return result;
+  };
+
+  Optional<APInt> umin, umax, smin, smax;
+  std::tie(umin, umax) =
+      minMaxBy(umul, {lhs.umin(), lhs.umax()}, {rhs.umin(), rhs.umax()},
+               /*signedCmp=*/false);
+  std::tie(smin, smax) =
+      minMaxBy(smul, {lhs.smin(), lhs.smax()}, {rhs.smin(), rhs.smax()},
+               /*signedCmp=*/true);
+
+  if (!lhs.umin() || !rhs.umin())
+    umin = {};
+  if (!lhs.umax() || !rhs.umax())
+    umax = {};
+  if (!canBoundBelow)
+    smin = {};
+  if (!canBoundAbove)
+    smax = {};
+  resultRanges.emplace_back(umin, umax, smin, smax);
+}
+
+/// Fix up division results (ex. for ceiling and floor), returning an APInt
+/// if there has been no overflow
+using DivisionFixupFn = llvm::function_ref<Optional<APInt>(
+    const APInt &lhs, const APInt &rhs, const APInt &result)>;
+
+static IntRangeAttrs inferDivUIRange(Type resultType, const IntRangeAttrs &lhs,
+                                     const IntRangeAttrs &rhs,
+                                     DivisionFixupFn fixup) {
+  Optional<APInt> lhsMin = lhs.umin();
+  Optional<APInt> lhsMax = lhs.umax();
+  Optional<APInt> rhsMin = rhs.umin();
+  Optional<APInt> rhsMax = rhs.umax();
+
+  unsigned int bitwidth = getAttrBitwidth(resultType);
+  if (rhsMin && !rhsMin->isZero()) {
+    if (!rhsMax) // Bound divisor above by 0xffff...fff to get lower bound of 0
+      rhsMax = APInt::getAllOnesValue(bitwidth);
+    auto udiv = [&fixup](auto &a, auto &b) -> Optional<APInt> {
+      return fixup(a, b, a.udiv(b));
+    };
+    auto urange = minMaxBy(udiv, {lhsMin, lhsMax}, {rhsMin, rhsMax},
+                           /*signedCmp=*/false);
+    if (!lhsMin)
+      urange.first = {};
+    if (!lhsMax)
+      urange.second = {};
+
+    return IntRangeAttrs::fromUnsigned(urange);
+  }
+  // Otherwise, it's possible we might divide by 0.
+  return {};
+}
+
+void arith::DivUIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type resultType = getResult().getType();
+  resultRanges.push_back(inferDivUIRange(
+      resultType, argRanges[0], argRanges[1],
+      [](auto &lhs, auto &rhs, auto &result) { return result; }));
+}
+
+static IntRangeAttrs inferDivSIRange(Type resultType, const IntRangeAttrs &lhs,
+                                     const IntRangeAttrs &rhs,
+                                     DivisionFixupFn fixup) {
+  Optional<APInt> lhsMin = lhs.smin();
+  Optional<APInt> lhsMax = lhs.smax();
+  Optional<APInt> rhsMin = rhs.smin();
+  Optional<APInt> rhsMax = rhs.smax();
+  bool canBoundBelow = rhsMin && rhsMin->isStrictlyPositive();
+  bool canBoundAbove = rhsMax && rhsMax->isNegative();
+  bool canDivide = canBoundBelow || canBoundAbove;
+
+  if (canDivide) {
+    unsigned int bitwidth = getAttrBitwidth(resultType);
+    // Unbounded below + negative upper bound -> lower bound = INT_MIN
+    if (!rhsMin)
+      rhsMin = APInt::getSignedMinValue(bitwidth);
+    // Unbounded above + positive lower bound -> upper bound = INT_MAX
+    if (!rhsMax)
+      rhsMax = APInt::getSignedMaxValue(bitwidth);
+    auto sdiv = [&fixup](auto &a, auto &b) -> Optional<APInt> {
+      bool overflowed = false;
+      APInt result = a.sdiv_ov(b, overflowed);
+      if (overflowed)
+        return {};
+      return fixup(a, b, result);
+    };
+    auto srange = minMaxBy(sdiv, {lhsMin, lhsMax}, {rhsMin, rhsMax},
+                           /*signedCmp=*/true);
+    if (!lhsMin)
+      srange.first = {};
+    if (!lhsMax)
+      srange.second = {};
+
+    return IntRangeAttrs::fromSigned(srange);
+  }
+  return {};
+}
+
+void arith::DivSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  resultRanges.push_back(inferDivSIRange(
+      getResult().getType(), argRanges[0], argRanges[1],
+      [](auto &lhs, auto &rhs, auto &result) { return result; }));
+}
+
+void arith::CeilDivUIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  DivisionFixupFn ceilDivUIFix = [](const APInt &lhs, const APInt &rhs,
+                                    const APInt &result) -> Optional<APInt> {
+    if (!lhs.urem(rhs).isZero()) {
+      bool overflowed = false;
+      APInt corrected =
+          result.uadd_ov(APInt(result.getBitWidth(), 1), overflowed);
+      if (overflowed)
+        return {};
+      return corrected;
+    }
+    return result;
+  };
+  Type resultType = getResult().getType();
+  resultRanges.push_back(inferDivUIRange(resultType, lhs, rhs, ceilDivUIFix));
+}
+
+void arith::CeilDivSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  Type resultType = getResult().getType();
+  DivisionFixupFn ceilDivSIFix = [](const APInt &lhs, const APInt &rhs,
+                                    const APInt &result) -> Optional<APInt> {
+    if (!lhs.srem(rhs).isZero() && lhs.isNonNegative() == rhs.isNonNegative()) {
+      bool overflowed = false;
+      APInt corrected =
+          result.sadd_ov(APInt(result.getBitWidth(), 1), overflowed);
+      if (overflowed)
+        return {};
+      return corrected;
+    }
+    return result;
+  };
+  resultRanges.push_back(inferDivSIRange(resultType, lhs, rhs, ceilDivSIFix));
+}
+
+void arith::FloorDivSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  Type resultType = getResult().getType();
+  DivisionFixupFn floorDivSIFix = [](const APInt &lhs, const APInt &rhs,
+                                     const APInt &result) -> Optional<APInt> {
+    if (!lhs.srem(rhs).isZero() && lhs.isNonNegative() != rhs.isNonNegative()) {
+      bool overflowed = false;
+      APInt corrected =
+          result.ssub_ov(APInt(result.getBitWidth(), 1), overflowed);
+      if (overflowed)
+        return {};
+      return corrected;
+    }
+    return result;
+  };
+  resultRanges.push_back(inferDivSIRange(resultType, lhs, rhs, floorDivSIFix));
+}
+
+void arith::RemUIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+  Optional<APInt> rhsMin = rhs.umin();
+  Optional<APInt> rhsMax = rhs.umax();
+  Optional<APInt> umin, umax;
+
+  if (rhsMin && rhsMax && !rhsMin->isZero()) {
+    APInt maxDivisor = *rhsMax;
+    umin = APInt::getZero(maxDivisor.getBitWidth());
+    umax = maxDivisor - 1;
+    // Special case: sweeping out a contiguous range in N/[modulus]
+    Optional<APInt> lhsMin = lhs.umin();
+    Optional<APInt> lhsMax = lhs.umax();
+    if (lhsMin && lhsMax && rhsMin == rhsMax) {
+      APInt minDividend = *lhsMin;
+      APInt maxDividend = *lhsMax;
+      if ((maxDividend - minDividend).ult(maxDivisor)) {
+        APInt minRem = minDividend.urem(maxDivisor);
+        APInt maxRem = maxDividend.urem(maxDivisor);
+        if (minRem.ule(maxRem)) {
+          umin = minRem;
+          umax = maxRem;
+        }
+      }
+    }
+  }
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(umin, umax));
+}
+
+void arith::RemSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+  Optional<APInt> lhsMin = lhs.smin();
+  Optional<APInt> lhsMax = lhs.smax();
+  Optional<APInt> rhsMin = rhs.smin();
+  Optional<APInt> rhsMax = rhs.smax();
+
+  Optional<APInt> smin, smax;
+  // No bounds if zero could be a divisor.
+  bool canBound = rhsMax && rhsMin &&
+                  (rhsMin->isStrictlyPositive() || rhsMax->isNegative());
+  if (canBound) {
+    APInt maxDivisor = rhsMin->isStrictlyPositive() ? *rhsMax : rhsMin->abs();
+    bool canNegativeDividend = !(lhsMin && lhsMin->isNonNegative());
+    bool canPositiveDividend = !(lhsMax && lhsMax->isNonPositive());
+    APInt zero = APInt::getZero(maxDivisor.getBitWidth());
+    APInt maxPositiveResult = maxDivisor - 1;
+    APInt minNegativeResult = -maxPositiveResult;
+    smin = canNegativeDividend ? minNegativeResult : zero;
+    smax = canPositiveDividend ? maxPositiveResult : zero;
+    // Special case: sweeping out a contiguous range in N/[modulus]
+    if (lhsMin && lhsMax && rhsMin == rhsMax) {
+      APInt minDividend = *lhsMin;
+      APInt maxDividend = *lhsMax;
+      if ((maxDividend - minDividend).ult(maxDivisor)) {
+        APInt minRem = minDividend.srem(maxDivisor);
+        APInt maxRem = maxDividend.srem(maxDivisor);
+        if (minRem.sle(maxRem)) {
+          smin = minRem;
+          smax = maxRem;
+        }
+      }
+    }
+  }
+  resultRanges.push_back(IntRangeAttrs::fromSigned(smin, smax));
+}
+
+/// "Widen" bounds - if 0bvvvvv??? <= a <= 0bvvvvv???,
+/// relax the bounds to 0bvvvvv000 <= a <= 0bvvvvv111, where vvvvv are the bits
+/// that both bonuds have in common. This gives us a consertive approximation
+/// for what values can be passed to bitwise operations. This will widen missing
+/// bounds to all zeroes / all ones so we can handle [unbounded] & 0xff => [0,
+/// 255].
+static IntAttrPair widenBitwiseBounds(Type resultType,
+                                      const IntRangeAttrs &bound) {
+  unsigned int bitwidth = getAttrBitwidth(resultType);
+  APInt leftVal = bound.umin().getValueOr(APInt::getZero(bitwidth));
+  APInt rightVal = bound.umax().getValueOr(APInt::getAllOnesValue(bitwidth));
+  unsigned int differingBits =
+      bitwidth - (leftVal ^ rightVal).countLeadingZeros();
+  leftVal.clearLowBits(differingBits);
+  rightVal.setLowBits(differingBits);
+  return {leftVal, rightVal};
+}
+
+void arith::AndIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type resultType = getResult().getType();
+  Optional<APInt> lhsZeros, lhsOnes, rhsZeros, rhsOnes;
+  std::tie(lhsZeros, lhsOnes) = widenBitwiseBounds(resultType, argRanges[0]);
+  std::tie(rhsZeros, rhsOnes) = widenBitwiseBounds(resultType, argRanges[1]);
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(
+      minMaxBy([](auto &a, auto &b) -> Optional<APInt> { return a & b; },
+               {lhsZeros, lhsOnes}, {rhsZeros, rhsOnes}, /*signedCmp=*/false)));
+}
+
+void arith::OrIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type resultType = getResult().getType();
+  Optional<APInt> lhsZeros, lhsOnes, rhsZeros, rhsOnes;
+  std::tie(lhsZeros, lhsOnes) = widenBitwiseBounds(resultType, argRanges[0]);
+  std::tie(rhsZeros, rhsOnes) = widenBitwiseBounds(resultType, argRanges[1]);
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(
+      minMaxBy([](auto &a, auto &b) -> Optional<APInt> { return a | b; },
+               {lhsZeros, lhsOnes}, {rhsZeros, rhsOnes}, /*signedCmp=*/false)));
+}
+
+void arith::XOrIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type resultType = getResult().getType();
+  Optional<APInt> lhsZeros, lhsOnes, rhsZeros, rhsOnes;
+  std::tie(lhsZeros, lhsOnes) = widenBitwiseBounds(resultType, argRanges[0]);
+  std::tie(rhsZeros, rhsOnes) = widenBitwiseBounds(resultType, argRanges[1]);
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(
+      minMaxBy([](auto &a, auto &b) -> Optional<APInt> { return a ^ b; },
+               {lhsZeros, lhsOnes}, {rhsZeros, rhsOnes}, /*signedCmp=*/false)));
+}
+
+void arith::MaxSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  Optional<APInt> smin;
+  // Take the largest lower bound (if any).
+  if (lhs.smin() && rhs.smin())
+    smin = lhs.smin()->sgt(*rhs.smin()) ? lhs.smin() : rhs.smin();
+  else if (lhs.smin())
+    smin = lhs.smin();
+  else if (rhs.smin())
+    smin = rhs.smin();
+
+  // If both upper bounds are present, take their max, be unbounded otherwise.
+  Optional<APInt> smax;
+  if (lhs.smax() && rhs.smax())
+    smax = lhs.smax()->sgt(*rhs.smax()) ? lhs.smax() : rhs.smax();
+  resultRanges.push_back(IntRangeAttrs::fromSigned(smin, smax));
+}
+
+void arith::MaxUIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  Optional<APInt> umin;
+  // Take the largest lower bound (if any).
+  if (lhs.umin() && rhs.umin())
+    umin = lhs.umin()->ugt(*rhs.umin()) ? lhs.umin() : rhs.umin();
+  else if (lhs.umin())
+    umin = lhs.umin();
+  else if (rhs.umin())
+    umin = rhs.umin();
+
+  // If both upper bounds are present, take their max, be unbounded otherwise.
+  Optional<APInt> umax;
+  if (lhs.umax() && rhs.umax())
+    umax = lhs.umax()->ugt(*rhs.umax()) ? lhs.umax() : rhs.umax();
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(umin, umax));
+}
+
+void arith::MinSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  Optional<APInt> smin;
+  // If both lower bounds are present, take their minimum.
+  if (lhs.smin() && rhs.smin())
+    smin = lhs.smin()->slt(*rhs.smin()) ? lhs.smin() : rhs.smin();
+
+  // For upper bounds, take the smallest (with absent -> +infinity).
+  Optional<APInt> smax;
+  if (lhs.smax() && rhs.smax())
+    smax = lhs.smax()->slt(*rhs.smax()) ? lhs.smax() : rhs.smax();
+  else if (lhs.smax())
+    smax = lhs.smax();
+  else if (rhs.smax())
+    smax = rhs.smax();
+  resultRanges.push_back(IntRangeAttrs::fromSigned(smin, smax));
+}
+
+void arith::MinUIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  Optional<APInt> umin;
+  // If both lower bounds are present, take their minimum.
+  if (lhs.umin() && rhs.umin())
+    umin = lhs.umin()->ult(*rhs.umin()) ? lhs.umin() : rhs.umin();
+
+  // For upper bounds, take the smallest (with absent -> +infinity).
+  Optional<APInt> umax;
+  if (lhs.umax() && rhs.umax())
+    umax = lhs.umax()->ult(*rhs.umax()) ? lhs.umax() : rhs.umax();
+  else if (lhs.umax())
+    umax = lhs.umax();
+  else if (rhs.umax())
+    umax = rhs.umax();
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(umin, umax));
+}
+
+void arith::ExtUIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type sourceType = getOperand().getType();
+  Type destType = getResult().getType();
+  unsigned int srcWidth = sourceType.getIntOrFloatBitWidth();
+  unsigned int destWidth = destType.getIntOrFloatBitWidth();
+  APInt umin = argRanges[0].umin().getValueOr(APInt::getZero(srcWidth));
+  APInt umax = argRanges[0].umax().getValueOr(APInt::getAllOnesValue(srcWidth));
+
+  umin = umin.zext(destWidth);
+  umax = umax.zext(destWidth);
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(umin, umax));
+}
+
+static IntRangeAttrs extSIRange(const IntRangeAttrs &range, Type sourceType,
+                                Type destType) {
+  unsigned int srcWidth = getAttrBitwidth(sourceType);
+  unsigned int destWidth = getAttrBitwidth(destType);
+  APInt smin = range.smin().getValueOr(APInt::getSignedMinValue(srcWidth));
+  APInt smax = range.smax().getValueOr(APInt::getSignedMaxValue(srcWidth));
+
+  smin = smin.sext(destWidth);
+  smax = smax.sext(destWidth);
+  return IntRangeAttrs::fromSigned(smin, smax);
+}
+
+void arith::ExtSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type sourceType = getOperand().getType();
+  Type destType = getResult().getType();
+  resultRanges.push_back(extSIRange(argRanges[0], sourceType, destType));
+}
+
+static IntRangeAttrs truncIRange(const IntRangeAttrs &range, Type destType) {
+  unsigned int destWidth = getAttrBitwidth(destType);
+  auto trunci = [destWidth](const APInt &val) -> APInt {
+    return val.trunc(destWidth);
+  };
+  Optional<APInt> umin = range.umin().map(trunci);
+  Optional<APInt> umax = range.umax().map(trunci);
+  Optional<APInt> smin = range.smin().map(trunci);
+  Optional<APInt> smax = range.smax().map(trunci);
+  return {umin, umax, smin, smax};
+}
+
+void arith::TruncIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type destType = getResult().getType();
+  resultRanges.push_back(truncIRange(argRanges[0], destType));
+}
+
+void arith::IndexCastOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Type sourceType = getOperand().getType();
+  Type destType = getResult().getType();
+  unsigned int srcWidth = getAttrBitwidth(sourceType);
+  unsigned int destWidth = getAttrBitwidth(destType);
+
+  if (srcWidth < destWidth)
+    resultRanges.push_back(extSIRange(argRanges[0], sourceType, destType));
+  else if (srcWidth > destWidth)
+    resultRanges.push_back(truncIRange(argRanges[0], destType));
+  else
+    resultRanges.push_back(argRanges[0]);
+}
+
+bool isStaticallyTrue(arith::CmpIPredicate pred, const IntRangeAttrs &lhs,
+                      const IntRangeAttrs &rhs) {
+  switch (pred) {
+  case arith::CmpIPredicate::sle:
+  case arith::CmpIPredicate::slt:
+    return (lhs.smax() && rhs.smin() &&
+            applyCmpPredicate(pred, *lhs.smax(), *rhs.smin()));
+  case arith::CmpIPredicate::ule:
+  case arith::CmpIPredicate::ult:
+    return (lhs.umax() && rhs.umin() &&
+            applyCmpPredicate(pred, *lhs.umax(), *rhs.umin()));
+  case arith::CmpIPredicate::sge:
+  case arith::CmpIPredicate::sgt:
+    return (lhs.smin() && rhs.smax() &&
+            applyCmpPredicate(pred, *lhs.smin(), *rhs.smax()));
+  case arith::CmpIPredicate::uge:
+  case arith::CmpIPredicate::ugt:
+    return (lhs.umin() && rhs.umax() &&
+            applyCmpPredicate(pred, *lhs.umin(), *rhs.umax()));
+  case arith::CmpIPredicate::eq: {
+    Optional<APInt> lhsConst = lhs.getConstantValue();
+    Optional<APInt> rhsConst = rhs.getConstantValue();
+    return lhsConst && rhsConst && lhsConst == rhsConst;
+  }
+  case arith::CmpIPredicate::ne: {
+    // While equality requires that there is an interpration of the preceeding
+    // computations that produces equal constants, whether that be signed or
+    // unsigned, statically determining inequality requires that neither
+    // interpretation produce potentially overlapping ranges.
+    bool sne = isStaticallyTrue(CmpIPredicate::slt, lhs, rhs) ||
+               isStaticallyTrue(CmpIPredicate::sgt, lhs, rhs);
+    bool une = isStaticallyTrue(CmpIPredicate::ult, lhs, rhs) ||
+               isStaticallyTrue(CmpIPredicate::ugt, lhs, rhs);
+    return sne && une;
+  }
+  }
+  return false;
+}
+
+void arith::CmpIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  arith::CmpIPredicate pred = getPredicate();
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+
+  Optional<APInt> value;
+  if (isStaticallyTrue(pred, lhs, rhs))
+    value = APInt::getAllOnesValue(1);
+  else if (isStaticallyTrue(invertPredicate(pred), lhs, rhs))
+    value = APInt::getZero(1);
+
+  resultRanges.push_back(IntRangeAttrs::range(value, value));
+}
+
+void arith::CmpFOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  // Can't infer anything about floats.
+  resultRanges.emplace_back();
+}
+
+void arith::SelectOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  Optional<APInt> mbCondVal = argRanges[0].getConstantValue();
+
+  if (mbCondVal) {
+    if (mbCondVal->isZero())
+      resultRanges.push_back(argRanges[2]);
+    else
+      resultRanges.push_back(argRanges[1]);
+    return;
+  }
+  resultRanges.push_back(IntRangeAttrs::join(argRanges[1], argRanges[2]));
+}
+
+void arith::ShLIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+  if (!rhs.umin() || !rhs.umax()) {
+    resultRanges.emplace_back();
+    return;
+  }
+
+  ConstArithFn shl = [](auto &l, auto &r) -> Optional<APInt> {
+    if (r.uge(r.getBitWidth()))
+      return {};
+    return l.shl(r);
+  };
+  Optional<APInt> umin, umax, smin, smax;
+  std::tie(umin, umax) =
+      minMaxBy(shl, {lhs.umin(), lhs.umax()}, {rhs.umin(), rhs.umax()},
+               /*signedCmp=*/false);
+  std::tie(smin, smax) =
+      minMaxBy(shl, {lhs.smin(), lhs.smax()}, {rhs.umin(), rhs.umax()},
+               /*signedCmp=*/true);
+  if (!lhs.umin())
+    umin = {};
+  if (!lhs.umax())
+    umax = {};
+  if (!lhs.smin())
+    smin = {};
+  if (!lhs.smax())
+    smax = {};
+
+  resultRanges.emplace_back(umin, umax, smin, smax);
+}
+
+void arith::ShRUIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+  if (!rhs.umin() || !rhs.umax()) {
+    resultRanges.emplace_back();
+    return;
+  }
+
+  ConstArithFn lshr = [](auto &l, auto &r) -> Optional<APInt> {
+    if (r.uge(r.getBitWidth()))
+      return {};
+    return l.lshr(r);
+  };
+  Optional<APInt> umin, umax;
+  std::tie(umin, umax) =
+      minMaxBy(lshr, {lhs.umin(), lhs.umax()}, {rhs.umin(), rhs.umax()},
+               /*signedCmp=*/false);
+  if (!lhs.umin())
+    umin = {};
+  if (!lhs.umax())
+    umax = {};
+
+  resultRanges.push_back(IntRangeAttrs::fromUnsigned(umin, umax));
+}
+
+void arith::ShRSIOp::inferResultRanges(
+    ArrayRef<IntRangeAttrs> argRanges,
+    SmallVectorImpl<IntRangeAttrs> &resultRanges) {
+  const IntRangeAttrs &lhs = argRanges[0];
+  const IntRangeAttrs &rhs = argRanges[1];
+  if (!rhs.umin() || !rhs.umax()) {
+    resultRanges.emplace_back();
+    return;
+  }
+
+  ConstArithFn ashr = [](auto &l, auto &r) -> Optional<APInt> {
+    if (r.uge(r.getBitWidth()))
+      return {};
+    return l.ashr(r);
+  };
+  Optional<APInt> smin, smax;
+  std::tie(smin, smax) = minMaxBy(ashr, {lhs.smin(), lhs.smax()},
+                                  {rhs.umin(), rhs.umax()}, /*signedCmp=*/true);
+  if (!lhs.smin())
+    smin = {};
+  if (!lhs.smax())
+    smax = {};
+
+  resultRanges.push_back(IntRangeAttrs::fromSigned(smin, smax));
+}
diff --git a/mlir/test/Dialect/Arithmetic/fold-inferred-constants.mlir b/mlir/test/Dialect/Arithmetic/fold-inferred-constants.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Dialect/Arithmetic/fold-inferred-constants.mlir
@@ -0,0 +1,626 @@
+// RUN: mlir-opt -arith-fold-inferred-constants -canonicalize %s | FileCheck %s
+
+// CHECK-LABEL: func @add_min_max
+// CHECK: %[[c3:.*]] = arith.constant 3 : index
+// CHECK: return %[[c3]]
+func @add_min_max(%a: index, %b: index) -> index {
+    %c1 = arith.constant 1 : index
+    %c2 = arith.constant 2 : index
+    %0 = arith.minsi %a, %c1 : index
+    %1 = arith.maxsi %0, %c1 : index
+    %2 = arith.minui %b, %c2 : index
+    %3 = arith.maxui %2, %c2 : index
+    %4 = arith.addi %1, %3 : index
+    return %4 : index
+}
+
+// CHECK-LABEL: func @add_lower_bound
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @add_lower_bound(%a : i32, %b : i32) -> i1 {
+    %c1 = arith.constant 1 : i32
+    %c2 = arith.constant 2 : i32
+    %0 = arith.maxsi %a, %c1 : i32
+    %1 = arith.maxsi %b, %c1 : i32
+    %2 = arith.addi %0, %1 : i32
+    %3 = arith.cmpi sge, %2, %c2 : i32
+    %4 = arith.cmpi uge, %2, %c2 : i32
+    %5 = arith.andi %3, %4 : i1
+    return %5 : i1
+}
+
+// CHECK-LABEL: func @sub_signed_vs_unsigned
+// CHECK-NOT: arith.cmpi sle
+// CHECK: %[[unsigned:.*]] = arith.cmpi ule
+// CHECK: return %[[unsigned]] : i1
+func @sub_signed_vs_unsigned(%v : i64) -> i1 {
+    %c0 = arith.constant 0 : i64
+    %c2 = arith.constant 2 : i64
+    %0 = arith.minsi %v, %c2 : i64
+    %1 = arith.subi %0, %c2 : i64
+    %2 = arith.cmpi sle, %1, %c0 : i64
+    %3 = arith.cmpi ule, %1, %c0 : i64
+    %4 = arith.andi %2, %3 : i1
+    return %4 : i1
+}
+
+// CHECK-LABEL: func @multiply_negatives
+// CHECK: %[[false:.*]] = arith.constant false
+// CHECK: return %[[false]]
+func @multiply_negatives(%a : index, %b : index) -> i1 {
+    %c2 = arith.constant 2 : index
+    %c3 = arith.constant 3 : index
+    %c_1 = arith.constant -1 : index
+    %c_2 = arith.constant -2 : index
+    %c_4 = arith.constant -4 : index
+    %c_12 = arith.constant -12 : index
+    %0 = arith.maxsi %a, %c2 : index
+    %1 = arith.minsi %0, %c3 : index
+    %2 = arith.minsi %b, %c_1 : index
+    %3 = arith.maxsi %2, %c_4 : index
+    %4 = arith.muli %1, %3 : index
+    %5 = arith.cmpi slt, %4, %c_12 : index
+    %6 = arith.cmpi slt, %c_1, %4 : index
+    %7 = arith.ori %5, %6 : i1
+    return %7 : i1
+}
+
+// CHECK-LABEL: func @multiply_unsigned_bounds
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @multiply_unsigned_bounds(%a : i16, %b : i16) -> i1 {
+    %c0 = arith.constant 0 : i16
+    %c4 = arith.constant 4 : i16
+    %c_mask = arith.constant 0x3fff : i16
+    %c_bound = arith.constant 0xfffc : i16
+    %0 = arith.andi %a, %c_mask : i16
+    %1 = arith.minui %b, %c4 : i16
+    %2 = arith.muli %0, %1 : i16
+    %3 = arith.cmpi uge, %2, %c0 : i16
+    %4 = arith.cmpi ule, %2, %c_bound : i16
+    %5 = arith.andi %3, %4 : i1
+    return %5 : i1
+}
+
+// CHECK-LABEL: @for_loop_with_increasing_arg
+// CHECK: %[[ret:.*]] = arith.cmpi ule
+// CHECK: return %[[ret]]
+func @for_loop_with_increasing_arg() -> i1 {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %c4 = arith.constant 4 : index
+    %c16 = arith.constant 16 : index
+    %0 = scf.for %arg0 = %c0 to %c4 step %c1 iter_args(%arg1 = %c0) -> index {
+        %10 = arith.addi %arg0, %arg1 : index
+        scf.yield %10 : index
+    }
+    %1 = arith.cmpi ule, %0, %c16 : index
+    return %1 : i1
+}
+
+// CHECK-LABEL: @for_loop_with_constant_result
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @for_loop_with_constant_result() -> i1 {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %c4 = arith.constant 4 : index
+    %true = arith.constant true
+    %0 = scf.for %arg0 = %c0 to %c4 step %c1 iter_args(%arg1 = %true) -> i1 {
+        %10 = arith.cmpi ule, %arg0, %c4 : index
+        %11 = arith.andi %10, %arg1 : i1
+        scf.yield %11 : i1
+    }
+    return %0 : i1
+}
+
+// CHECK-LABEL: func @div_bounds_positive
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @div_bounds_positive(%arg0 : index) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c2 = arith.constant 2 : index
+    %c4 = arith.constant 4 : index
+    %0 = arith.maxsi %arg0, %c2 : index
+    %1 = arith.divsi %c4, %0 : index
+    %2 = arith.divui %c4, %0 : index
+
+    %3 = arith.cmpi sge, %1, %c0 : index
+    %4 = arith.cmpi sle, %1, %c2 : index
+    %5 = arith.cmpi sge, %2, %c0 : index
+    %6 = arith.cmpi sle, %1, %c2 : index
+
+    %7 = arith.andi %3, %4 : i1
+    %8 = arith.andi %7, %5 : i1
+    %9 = arith.andi %8, %6 : i1
+    return %9 : i1
+}
+
+// CHECK-LABEL: func @div_bounds_negative
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @div_bounds_negative(%arg0 : index) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c_2 = arith.constant -2 : index
+    %c4 = arith.constant 4 : index
+    %0 = arith.minsi %arg0, %c_2 : index
+    %1 = arith.divsi %c4, %0 : index
+    %2 = arith.divui %c4, %0 : index
+
+    %3 = arith.cmpi sle, %1, %c0 : index
+    %4 = arith.cmpi sge, %1, %c_2 : index
+    %5 = arith.cmpi eq, %2, %c0 : index
+
+    %7 = arith.andi %3, %4 : i1
+    %8 = arith.andi %7, %5 : i1
+    return %8 : i1
+}
+
+// CHECK-LABEL: func @div_zero_undefined
+// CHECK: %[[ret:.*]] = arith.cmpi ule
+// CHECK: return %[[ret]]
+func @div_zero_undefined(%arg0 : index) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %c4 = arith.constant 4 : index
+    %0 = arith.andi %arg0, %c1 : index
+    %1 = arith.divui %c4, %0 : index
+    %2 = arith.cmpi ule, %1, %c4 : index
+    return %2 : i1
+}
+
+// CHECK-LABEL: func @ceil_divui
+// CHECK: %[[ret:.*]] = arith.cmpi eq
+// CHECK: return %[[ret]]
+func @ceil_divui(%arg0 : index) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %c3 = arith.constant 3 : index
+    %c4 = arith.constant 4 : index
+
+    %0 = arith.minui %arg0, %c3 : index
+    %1 = arith.maxui %0, %c1 : index
+    %2 = arith.ceildivui %1, %c4 : index
+    %3 = arith.cmpi eq, %2, %c1 : index
+
+    %4 = arith.maxui %0, %c0 : index
+    %5 = arith.ceildivui %4, %c4 : index
+    %6 = arith.cmpi eq, %5, %c1 : index
+    %7 = arith.andi %3, %6 : i1
+    return %7 : i1
+}
+
+// CHECK-LABEL: func @ceil_divsi
+// CHECK: %[[ret:.*]] = arith.cmpi eq
+// CHECK: return %[[ret]]
+func @ceil_divsi(%arg0 : index) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %c3 = arith.constant 3 : index
+    %c4 = arith.constant 4 : index
+    %c-4 = arith.constant -4 : index
+
+    %0 = arith.minsi %arg0, %c3 : index
+    %1 = arith.maxsi %0, %c1 : index
+    %2 = arith.ceildivsi %1, %c4 : index
+    %3 = arith.cmpi eq, %2, %c1 : index
+    %4 = arith.ceildivsi %1, %c-4 : index
+    %5 = arith.cmpi eq, %4, %c0 : index
+    %6 = arith.andi %3, %5 : i1
+
+    %7 = arith.maxsi %0, %c0 : index
+    %8 = arith.ceildivsi %7, %c4 : index
+    %9 = arith.cmpi eq, %8, %c1 : index
+    %10 = arith.andi %6, %9 : i1
+    return %10 : i1
+}
+
+// CHECK-LABEL: func @floor_divsi
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @floor_divsi(%arg0 : index) -> i1 {
+    %c4 = arith.constant 4 : index
+    %c-1 = arith.constant -1 : index
+    %c-3 = arith.constant -3 : index
+    %c-4 = arith.constant -4 : index
+
+    %0 = arith.minsi %arg0, %c-1 : index
+    %1 = arith.maxsi %0, %c-4 : index
+    %2 = arith.floordivsi %1, %c4 : index
+    %3 = arith.cmpi eq, %2, %c-1 : index
+    return %3 : i1
+}
+
+// CHECK-LABEL: func @remui_base
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @remui_base(%arg0 : index, %arg1 : index ) -> i1 {
+    %c2 = arith.constant 2 : index
+    %c4 = arith.constant 4 : index
+
+    %0 = arith.minui %arg1, %c4 : index
+    %1 = arith.maxui %0, %c2 : index
+    %2 = arith.remui %arg0, %1 : index
+    %3 = arith.cmpi ult, %2, %c4 : index
+    return %3 : i1
+}
+
+// CHECK-LABEL: func @remsi_base
+// CHECK: %[[ret:.*]] = arith.cmpi sge
+// CHECK: return %[[ret]]
+func @remsi_base(%arg0 : index, %arg1 : index ) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c2 = arith.constant 2 : index
+    %c4 = arith.constant 4 : index
+    %c-4 = arith.constant -4 : index
+    %true = arith.constant true
+
+    %0 = arith.minsi %arg1, %c4 : index
+    %1 = arith.maxsi %0, %c2 : index
+    %2 = arith.remsi %arg0, %1 : index
+    %3 = arith.cmpi sgt, %2, %c-4 : index
+    %4 = arith.cmpi slt, %2, %c4 : index
+    %5 = arith.cmpi sge, %2, %c0 : index
+    %6 = arith.andi %3, %4 : i1
+    %7 = arith.andi %5, %6 : i1
+    return %7 : i1
+}
+
+// CHECK-LABEL: func @remsi_positive
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @remsi_positive(%arg0 : index, %arg1 : index ) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c2 = arith.constant 2 : index
+    %c4 = arith.constant 4 : index
+    %true = arith.constant true
+
+    %0 = arith.minsi %arg1, %c4 : index
+    %1 = arith.maxsi %0, %c2 : index
+    %2 = arith.maxsi %arg0, %c0 : index
+    %3 = arith.remsi %2, %1 : index
+    %4 = arith.cmpi sge, %3, %c0 : index
+    %5 = arith.cmpi slt, %3, %c4 : index
+    %6 = arith.andi %4, %5 : i1
+    return %6 : i1
+}
+
+// CHECK-LABEL: func @remui_restricted
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @remui_restricted(%arg0 : index) -> i1 {
+    %c2 = arith.constant 2 : index
+    %c3 = arith.constant 3 : index
+    %c4 = arith.constant 4 : index
+
+    %0 = arith.minui %arg0, %c3 : index
+    %1 = arith.maxui %0, %c2 : index
+    %2 = arith.remui %1, %c4 : index
+    %3 = arith.cmpi ule, %2, %c3 : index
+    %4 = arith.cmpi uge, %2, %c2 : index
+    %5 = arith.andi %3, %4 : i1
+    return %5 : i1
+}
+
+// CHECK-LABEL: func @remsi_restricted
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @remsi_restricted(%arg0 : index) -> i1 {
+    %c2 = arith.constant 2 : index
+    %c3 = arith.constant 3 : index
+    %c-4 = arith.constant -4 : index
+
+    %0 = arith.minsi %arg0, %c3 : index
+    %1 = arith.maxsi %0, %c2 : index
+    %2 = arith.remsi %1, %c-4 : index
+    %3 = arith.cmpi ule, %2, %c3 : index
+    %4 = arith.cmpi uge, %2, %c2 : index
+    %5 = arith.andi %3, %4 : i1
+    return %5 : i1
+}
+
+// CHECK-LABEL: func @remui_restricted_fails
+// CHECK: %[[ret:.*]] = arith.cmpi ne
+// CHECK: return %[[ret]]
+func @remui_restricted_fails(%arg0 : index) -> i1 {
+    %c2 = arith.constant 2 : index
+    %c3 = arith.constant 3 : index
+    %c4 = arith.constant 4 : index
+    %c5 = arith.constant 5 : index
+
+    %0 = arith.minui %arg0, %c5 : index
+    %1 = arith.maxui %0, %c3 : index
+    %2 = arith.remui %1, %c4 : index
+    %3 = arith.cmpi ne, %2, %c2 : index
+    return %3 : i1
+}
+
+// CHECK-LABEL: func @remsi_restricted_fails
+// CHECK: %[[ret:.*]] = arith.cmpi ne
+// CHECK: return %[[ret]]
+func @remsi_restricted_fails(%arg0 : index) -> i1 {
+    %c2 = arith.constant 2 : index
+    %c3 = arith.constant 3 : index
+    %c5 = arith.constant 5 : index
+    %c-4 = arith.constant -4 : index
+
+    %0 = arith.minsi %arg0, %c5 : index
+    %1 = arith.maxsi %0, %c3 : index
+    %2 = arith.remsi %1, %c-4 : index
+    %3 = arith.cmpi ne, %2, %c2 : index
+    return %3 : i1
+}
+
+// CHECK-LABEL: func @andi
+// CHECK: %[[ret:.*]] = arith.cmpi ugt
+// CHECK: return %[[ret]]
+func @andi(%arg0 : index) -> i1 {
+    %c2 = arith.constant 2 : index
+    %c5 = arith.constant 5 : index
+    %c7 = arith.constant 7 : index
+
+    %0 = arith.minsi %arg0, %c5 : index
+    %1 = arith.maxsi %0, %c2 : index
+    %2 = arith.andi %1, %c7 : index
+    %3 = arith.cmpi ugt, %2, %c5 : index
+    %4 = arith.cmpi ule, %2, %c7 : index
+    %5 = arith.andi %3, %4 : i1
+    return %5 : i1
+}
+
+// CHECK-LABEL: func @andi_doesnt_make_nonnegative
+// CHECK: %[[ret:.*]] = arith.cmpi sge
+// CHECK: return %[[ret]]
+func @andi_doesnt_make_nonnegative(%arg0 : index) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %0 = arith.addi %arg0, %c1 : index
+    %1 = arith.andi %arg0, %0 : index
+    %2 = arith.cmpi sge, %1, %c0 : index
+    return %2 : i1
+}
+
+
+// CHECK-LABEL: func @ori
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @ori(%arg0 : i128, %arg1 : i128) -> i1 {
+    %c-1 = arith.constant -1 : i128
+    %c0 = arith.constant 0 : i128
+
+    %0 = arith.minsi %arg1, %c-1 : i128
+    %1 = arith.ori %arg0, %0 : i128
+    %2 = arith.cmpi slt, %1, %c0 : i128
+    return %2 : i1
+}
+
+// CHECK-LABEL: func @xori
+// CHECK: %[[false:.*]] = arith.constant false
+// CHECK: return %[[false]]
+func @xori(%arg0 : i64, %arg1 : i64) -> i1 {
+    %c0 = arith.constant 0 : i64
+    %c7 = arith.constant 7 : i64
+    %c15 = arith.constant 15 : i64
+    %true = arith.constant true
+
+    %0 = arith.minui %arg0, %c7 : i64
+    %1 = arith.minui %arg1, %c15 : i64
+    %2 = arith.xori %0, %1 : i64
+    %3 = arith.cmpi sle, %2, %c15 : i64
+    %4 = arith.xori %3, %true : i1
+    return %4 : i1
+}
+
+// CHECK-LABEL: func @extui
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @extui(%arg0 : i16) -> i1 {
+    %ci16_max = arith.constant 0xffff : i32
+    %0 = arith.extui %arg0 : i16 to i32
+    %1 = arith.cmpi ule, %0, %ci16_max : i32
+    return %1 : i1
+}
+
+// CHECK-LABEL: func @extsi
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @extsi(%arg0 : i16) -> i1 {
+    %ci16_smax = arith.constant 0x7fff : i32
+    %ci16_smin = arith.constant 0xffff8000 : i32
+    %0 = arith.extsi %arg0 : i16 to i32
+    %1 = arith.cmpi sle, %0, %ci16_smax : i32
+    %2 = arith.cmpi sge, %0, %ci16_smin : i32
+    %3 = arith.andi %1, %2 : i1
+    return %3 : i1
+}
+
+// CHECK-LABEL: func @trunci
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @trunci(%arg0 : i32) -> i1 {
+    %c-14_i32 = arith.constant -14 : i32
+    %c-14_i16 = arith.constant -14 : i16
+    %ci16_smin = arith.constant 0xffff8000 : i32
+    %0 = arith.minsi %arg0, %c-14_i32 : i32
+    %1 = arith.trunci %0 : i32 to i16
+    %2 = arith.cmpi sle, %1, %c-14_i16 : i16
+    %3 = arith.extsi %1 : i16 to i32
+    %4 = arith.cmpi sle, %3, %c-14_i32 : i32
+    %5 = arith.cmpi sge, %3, %ci16_smin : i32
+    %6 = arith.andi %2, %4 : i1
+    %7 = arith.andi %6, %5 : i1
+    return %7 : i1
+}
+
+// CHECK-LABEL: func @index_cast
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @index_cast(%arg0 : index) -> i1 {
+    %ci32_smin = arith.constant 0xffffffff80000000 : i64
+    %0 = arith.index_cast %arg0 : index to i32
+    %1 = arith.index_cast %0 : i32 to index
+    %2 = arith.index_cast %ci32_smin : i64 to index
+    %3 = arith.cmpi sge, %1, %2 : index
+    return %3 : i1
+}
+
+// CHECK-LABEL: func @shli
+// CHECK: %[[ret:.*]] = arith.cmpi sgt
+// CHECK: return %[[ret]]
+func @shli(%arg0 : i32, %arg1 : i1) -> i1 {
+    %c2 = arith.constant 2 : i32
+    %c4 = arith.constant 4 : i32
+    %c8 = arith.constant 8 : i32
+    %c32 = arith.constant 32 : i32
+    %c-1 = arith.constant -1 : i32
+    %c-16 = arith.constant -16 : i32
+    %0 = arith.maxsi %arg0, %c-1 : i32
+    %1 = arith.minsi %0, %c2 : i32
+    %2 = arith.select %arg1, %c2, %c4 : i32
+    %3 = arith.shli %1, %2 : i32
+    %4 = arith.cmpi sge, %3, %c-16 : i32
+    %5 = arith.cmpi sle, %3, %c32 : i32
+    %6 = arith.cmpi sgt, %3, %c8 : i32
+    %7 = arith.andi %4, %5 : i1
+    %8 = arith.andi %7, %6 : i1
+    return %8 : i1
+}
+
+// CHECK-LABEL: func @shrui
+// CHECK: %[[ret:.*]] = arith.cmpi uge
+// CHECK: return %[[ret]]
+func @shrui(%arg0 : i1) -> i1 {
+    %c2 = arith.constant 2 : i32
+    %c4 = arith.constant 4 : i32
+    %c8 = arith.constant 8 : i32
+    %c32 = arith.constant 32 : i32
+    %0 = arith.select %arg0, %c2, %c4 : i32
+    %1 = arith.shrui %c32, %0 : i32
+    %2 = arith.cmpi ule, %1, %c8 : i32
+    %3 = arith.cmpi uge, %1, %c2 : i32
+    %4 = arith.cmpi uge, %1, %c8 : i32
+    %5 = arith.andi %2, %3 : i1
+    %6 = arith.andi %5, %4 : i1
+    return %6 : i1
+}
+
+// CHECK-LABEL: func @shrsi
+// CHECK: %[[ret:.*]] = arith.cmpi slt
+// CHECK: return %[[ret]]
+func @shrsi(%arg0 : i32, %arg1 : i1) -> i1 {
+    %c2 = arith.constant 2 : i32
+    %c4 = arith.constant 4 : i32
+    %c8 = arith.constant 8 : i32
+    %c32 = arith.constant 32 : i32
+    %c-8 = arith.constant -8 : i32
+    %c-32 = arith.constant -32 : i32
+    %0 = arith.maxsi %arg0, %c-32 : i32
+    %1 = arith.minsi %0, %c32 : i32
+    %2 = arith.select %arg1, %c2, %c4 : i32
+    %3 = arith.shrsi %1, %2 : i32
+    %4 = arith.cmpi sge, %3, %c-8 : i32
+    %5 = arith.cmpi sle, %3, %c8 : i32
+    %6 = arith.cmpi slt, %3, %c2 : i32
+    %7 = arith.andi %4, %5 : i1
+    %8 = arith.andi %7, %6 : i1
+    return %8 : i1
+}
+
+// CHECK-LABEL: func @no_aggressive_eq
+// CHECK: %[[ret:.*]] = arith.cmpi eq
+// CHECK: return %[[ret]]
+func @no_aggressive_eq(%arg0 : index) -> i1 {
+    %c1 = arith.constant 1 : index
+    %0 = arith.andi %arg0, %c1 : index
+    %1 = arith.minui %arg0, %c1 : index
+    %2 = arith.cmpi eq, %0, %1 : index
+    return %2 : i1
+}
+
+// CHECK-LABEL: func @select_union
+// CHECK: %[[ret:.*]] = arith.cmpi ne
+// CHECK: return %[[ret]]
+
+func @select_union(%arg0 : index, %arg1 : i1) -> i1 {
+    %c64 = arith.constant 64 : index
+    %c100 = arith.constant 100 : index
+    %c128 = arith.constant 128 : index
+    %c192 = arith.constant 192 : index
+    %0 = arith.remui %arg0, %c64 : index
+    %1 = arith.addi %0, %c128 : index
+    %2 = arith.select %arg1, %0, %1 : index
+    %3 = arith.cmpi slt, %2, %c192 : index
+    %4 = arith.cmpi ne, %c100, %2 : index
+    %5 = arith.andi %3, %4 : i1
+    return %5 : i1
+}
+
+// CHECK-LABEL: func @if_union
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @if_union(%arg0 : index, %arg1 : i1) -> i1 {
+    %c4 = arith.constant 4 : index
+    %c16 = arith.constant 16 : index
+    %c-1 = arith.constant -1 : index
+    %c-4 = arith.constant -4 : index
+    %0 = arith.minui %arg0, %c4 : index
+    %1 = scf.if %arg1 -> index {
+        %10 = arith.muli %0, %0 : index
+        scf.yield %10 : index
+    } else {
+        %20 = arith.muli %0, %c-1 : index
+        scf.yield %20 : index
+    }
+    %2 = arith.cmpi sle, %1, %c16 : index
+    %3 = arith.cmpi sge, %1, %c-4 : index
+    %4 = arith.andi %2, %3 : i1
+    return %4 : i1
+}
+
+// CHECK-LABEL: func @branch_union
+// CHECK: %[[true:.*]] = arith.constant true
+// CHECK: return %[[true]]
+func @branch_union(%arg0 : index, %arg1 : i1) -> i1 {
+    %c4 = arith.constant 4 : index
+    %c16 = arith.constant 16 : index
+    %c-1 = arith.constant -1 : index
+    %c-4 = arith.constant -4 : index
+    %0 = arith.minui %arg0, %c4 : index
+    cf.cond_br %arg1, ^bb1, ^bb2
+^bb1 :
+    %1 = arith.muli %0, %0 : index
+    cf.br ^bb3(%1 : index)
+^bb2 :
+    %2 = arith.muli %0, %c-1 : index
+    cf.br ^bb3(%2 : index)
+^bb3(%3 : index) :
+    %4 = arith.cmpi sle, %3, %c16 : index
+    %5 = arith.cmpi sge, %3, %c-4 : index
+    %6 = arith.andi %4, %5 : i1
+    return %6 : i1
+}
+
+// CHECK-LABEL: func @loop_bound_not_inferred_with_branch
+// CHECK-DAG: %[[min:.*]] = arith.cmpi sge
+// CHECK-DAG: %[[max:.*]] = arith.cmpi slt
+// CHECK-DAG: %[[ret:.*]] = arith.andi %[[min]], %[[max]]
+// CHECK: return %[[ret]]
+func @loop_bound_not_inferred_with_branch(%arg0 : index, %arg1 : i1) -> i1 {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %c4 = arith.constant 4 : index
+    %0 = arith.minui %arg0, %c4 : index
+    cf.br ^bb2(%c0 : index)
+^bb1(%1 : index) :
+    %2 = arith.addi %1, %c1 : index
+    cf.br ^bb2(%2 : index)
+^bb2(%3 : index):
+    %4 = arith.cmpi ult, %3, %c4 : index
+    cf.cond_br %4, ^bb1(%3 : index), ^bb3(%3 : index)
+^bb3(%5 : index) :
+    %6 = arith.cmpi sge, %5, %c0 : index
+    %7 = arith.cmpi slt, %5, %c4 : index
+    %8 = arith.andi %6, %7 : i1
+    return %8 : i1
+}
+