src/jit/RangeAnalysis.cpp

/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 * vim: set ts=8 sts=4 et sw=4 tw=99:
 * This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

#include "jit/RangeAnalysis.h"

#include "mozilla/MathAlgorithms.h"

#include "jit/Ion.h"
#include "jit/IonAnalysis.h"
#include "jit/JitSpewer.h"
#include "jit/MIR.h"
#include "jit/MIRGenerator.h"
#include "jit/MIRGraph.h"
#include "js/Conversions.h"
#include "vm/ArgumentsObject.h"
#include "vm/TypedArrayObject.h"

#include "vm/BytecodeUtil-inl.h"

using namespace js;
using namespace js::jit;

using JS::GenericNaN;
using JS::ToInt32;
using mozilla::Abs;
using mozilla::CountLeadingZeroes32;
using mozilla::ExponentComponent;
using mozilla::FloorLog2;
using mozilla::IsInfinite;
using mozilla::IsNaN;
using mozilla::IsNegativeZero;
using mozilla::NegativeInfinity;
using mozilla::NumberEqualsInt32;
using mozilla::PositiveInfinity;
using mozilla::Swap;

// This algorithm is based on the paper "Eliminating Range Checks Using
// Static Single Assignment Form" by Gough and Klaren.
//
// We associate a range object with each SSA name, and the ranges are consulted
// in order to determine whether overflow is possible for arithmetic
// computations.
//
// An important source of range information that requires care to take
// advantage of is conditional control flow. Consider the code below:
//
// if (x < 0) {
//   y = x + 2000000000;
// } else {
//   if (x < 1000000000) {
//     y = x * 2;
//   } else {
//     y = x - 3000000000;
//   }
// }
//
// The arithmetic operations in this code cannot overflow, but it is not
// sufficient to simply associate each name with a range, since the information
// differs between basic blocks. The traditional dataflow approach would be
// associate ranges with (name, basic block) pairs. This solution is not
// satisfying, since we lose the benefit of SSA form: in SSA form, each
// definition has a unique name, so there is no need to track information about
// the control flow of the program.
//
// The approach used here is to add a new form of pseudo operation called a
// beta node, which associates range information with a value. These beta
// instructions take one argument and additionally have an auxiliary constant
// range associated with them. Operationally, beta nodes are just copies, but
// the invariant expressed by beta node copies is that the output will fall
// inside the range given by the beta node.  Gough and Klaeren refer to SSA
// extended with these beta nodes as XSA form. The following shows the example
// code transformed into XSA form:
//
// if (x < 0) {
//   x1 = Beta(x, [INT_MIN, -1]);
//   y1 = x1 + 2000000000;
// } else {
//   x2 = Beta(x, [0, INT_MAX]);
//   if (x2 < 1000000000) {
//     x3 = Beta(x2, [INT_MIN, 999999999]);
//     y2 = x3*2;
//   } else {
//     x4 = Beta(x2, [1000000000, INT_MAX]);
//     y3 = x4 - 3000000000;
//   }
//   y4 = Phi(y2, y3);
// }
// y = Phi(y1, y4);
//
// We insert beta nodes for the purposes of range analysis (they might also be
// usefully used for other forms of bounds check elimination) and remove them
// after range analysis is performed. The remaining compiler phases do not ever
// encounter beta nodes.

static bool IsDominatedUse(MBasicBlock* block, MUse* use) {
  MNode* n = use->consumer();
  bool isPhi = n->isDefinition() && n->toDefinition()->isPhi();

  if (isPhi) {
    MPhi* phi = n->toDefinition()->toPhi();
    return block->dominates(phi->block()->getPredecessor(phi->indexOf(use)));
  }

  return block->dominates(n->block());
}

static inline void SpewRange(MDefinition* def) {
#ifdef JS_JITSPEW
  if (JitSpewEnabled(JitSpew_Range) && def->type() != MIRType::None &&
      def->range()) {
    JitSpewHeader(JitSpew_Range);
    Fprinter& out = JitSpewPrinter();
    def->printName(out);
    out.printf(" has range ");
    def->range()->dump(out);
  }
#endif
}

static inline void SpewTruncate(MDefinition* def,
                                MDefinition::TruncateKind kind,
                                bool shouldClone) {
#ifdef JS_JITSPEW
  if (JitSpewEnabled(JitSpew_Range)) {
    JitSpewHeader(JitSpew_Range);
    Fprinter& out = JitSpewPrinter();
    out.printf("truncating ");
    def->printName(out);
    out.printf(" (kind: %s, clone: %d)\n",
               MDefinition::TruncateKindString(kind), shouldClone);
  }
#endif
}

TempAllocator& RangeAnalysis::alloc() const { return graph_.alloc(); }

void RangeAnalysis::replaceDominatedUsesWith(MDefinition* orig,
                                             MDefinition* dom,
                                             MBasicBlock* block) {
  for (MUseIterator i(orig->usesBegin()); i != orig->usesEnd();) {
    MUse* use = *i++;
    if (use->consumer() != dom && IsDominatedUse(block, use))
      use->replaceProducer(dom);
  }
}

bool RangeAnalysis::addBetaNodes() {
  JitSpew(JitSpew_Range, "Adding beta nodes");

  for (PostorderIterator i(graph_.poBegin()); i != graph_.poEnd(); i++) {
    MBasicBlock* block = *i;
    JitSpew(JitSpew_Range, "Looking at block %d", block->id());

    BranchDirection branch_dir;
    MTest* test = block->immediateDominatorBranch(&branch_dir);

    if (!test || !test->getOperand(0)->isCompare()) continue;

    MCompare* compare = test->getOperand(0)->toCompare();

    if (!compare->isNumericComparison()) continue;

    // TODO: support unsigned comparisons
    if (compare->compareType() == MCompare::Compare_UInt32) continue;

    MDefinition* left = compare->getOperand(0);
    MDefinition* right = compare->getOperand(1);
    double bound;
    double conservativeLower = NegativeInfinity<double>();
    double conservativeUpper = PositiveInfinity<double>();
    MDefinition* val = nullptr;

    JSOp jsop = compare->jsop();

    if (branch_dir == FALSE_BRANCH) {
      jsop = NegateCompareOp(jsop);
      conservativeLower = GenericNaN();
      conservativeUpper = GenericNaN();
    }

    MConstant* leftConst = left->maybeConstantValue();
    MConstant* rightConst = right->maybeConstantValue();
    if (leftConst && leftConst->isTypeRepresentableAsDouble()) {
      bound = leftConst->numberToDouble();
      val = right;
      jsop = ReverseCompareOp(jsop);
    } else if (rightConst && rightConst->isTypeRepresentableAsDouble()) {
      bound = rightConst->numberToDouble();
      val = left;
    } else if (left->type() == MIRType::Int32 &&
               right->type() == MIRType::Int32) {
      MDefinition* smaller = nullptr;
      MDefinition* greater = nullptr;
      if (jsop == JSOP_LT) {
        smaller = left;
        greater = right;
      } else if (jsop == JSOP_GT) {
        smaller = right;
        greater = left;
      }
      if (smaller && greater) {
        if (!alloc().ensureBallast()) return false;

        MBeta* beta;
        beta = MBeta::New(
            alloc(), smaller,
            Range::NewInt32Range(alloc(), JSVAL_INT_MIN, JSVAL_INT_MAX - 1));
        block->insertBefore(*block->begin(), beta);
        replaceDominatedUsesWith(smaller, beta, block);
        JitSpew(JitSpew_Range, "Adding beta node for smaller %d",
                smaller->id());
        beta = MBeta::New(
            alloc(), greater,
            Range::NewInt32Range(alloc(), JSVAL_INT_MIN + 1, JSVAL_INT_MAX));
        block->insertBefore(*block->begin(), beta);
        replaceDominatedUsesWith(greater, beta, block);
        JitSpew(JitSpew_Range, "Adding beta node for greater %d",
                greater->id());
      }
      continue;
    } else {
      continue;
    }

    // At this point, one of the operands if the compare is a constant, and
    // val is the other operand.
    MOZ_ASSERT(val);

    Range comp;
    switch (jsop) {
      case JSOP_LE:
        comp.setDouble(conservativeLower, bound);
        break;
      case JSOP_LT:
        // For integers, if x < c, the upper bound of x is c-1.
        if (val->type() == MIRType::Int32) {
          int32_t intbound;
          if (NumberEqualsInt32(bound, &intbound) &&
              SafeSub(intbound, 1, &intbound))
            bound = intbound;
        }
        comp.setDouble(conservativeLower, bound);

        // Negative zero is not less than zero.
        if (bound == 0) comp.refineToExcludeNegativeZero();
        break;
      case JSOP_GE:
        comp.setDouble(bound, conservativeUpper);
        break;
      case JSOP_GT:
        // For integers, if x > c, the lower bound of x is c+1.
        if (val->type() == MIRType::Int32) {
          int32_t intbound;
          if (NumberEqualsInt32(bound, &intbound) &&
              SafeAdd(intbound, 1, &intbound))
            bound = intbound;
        }
        comp.setDouble(bound, conservativeUpper);

        // Negative zero is not greater than zero.
        if (bound == 0) comp.refineToExcludeNegativeZero();
        break;
      case JSOP_STRICTEQ:
        // A strict comparison can test for things other than numeric value.
        if (!compare->isNumericComparison()) continue;
        // Otherwise fall through to handle JSOP_STRICTEQ the same as JSOP_EQ.
        MOZ_FALLTHROUGH;
      case JSOP_EQ:
        comp.setDouble(bound, bound);
        break;
      case JSOP_STRICTNE:
        // A strict comparison can test for things other than numeric value.
        if (!compare->isNumericComparison()) continue;
        // Otherwise fall through to handle JSOP_STRICTNE the same as JSOP_NE.
        MOZ_FALLTHROUGH;
      case JSOP_NE:
        // Negative zero is not not-equal to zero.
        if (bound == 0) {
          comp.refineToExcludeNegativeZero();
          break;
        }
        continue;  // well, we could have
                   // [-\inf, bound-1] U [bound+1, \inf] but we only use
                   // contiguous ranges.
      default:
        continue;
    }

    if (JitSpewEnabled(JitSpew_Range)) {
      JitSpewHeader(JitSpew_Range);
      Fprinter& out = JitSpewPrinter();
      out.printf("Adding beta node for %d with range ", val->id());
      comp.dump(out);
    }

    if (!alloc().ensureBallast()) return false;

    MBeta* beta = MBeta::New(alloc(), val, new (alloc()) Range(comp));
    block->insertBefore(*block->begin(), beta);
    replaceDominatedUsesWith(val, beta, block);
  }

  return true;
}

bool RangeAnalysis::removeBetaNodes() {
  JitSpew(JitSpew_Range, "Removing beta nodes");

  for (PostorderIterator i(graph_.poBegin()); i != graph_.poEnd(); i++) {
    MBasicBlock* block = *i;
    for (MDefinitionIterator iter(*i); iter;) {
      MDefinition* def = *iter++;
      if (def->isBeta()) {
        MDefinition* op = def->getOperand(0);
        JitSpew(JitSpew_Range, "Removing beta node %d for %d", def->id(),
                op->id());
        def->justReplaceAllUsesWith(op);
        block->discardDef(def);
      } else {
        // We only place Beta nodes at the beginning of basic
        // blocks, so if we see something else, we can move on
        // to the next block.
        break;
      }
    }
  }
  return true;
}

void SymbolicBound::dump(GenericPrinter& out) const {
  if (loop) out.printf("[loop] ");
  sum.dump(out);
}

void SymbolicBound::dump() const {
  Fprinter out(stderr);
  dump(out);
  out.printf("\n");
  out.finish();
}

// Test whether the given range's exponent tells us anything that its lower
// and upper bound values don't.
static bool IsExponentInteresting(const Range* r) {
  // If it lacks either a lower or upper bound, the exponent is interesting.
  if (!r->hasInt32Bounds()) return true;

  // Otherwise if there's no fractional part, the lower and upper bounds,
  // which are integers, are perfectly precise.
  if (!r->canHaveFractionalPart()) return false;

  // Otherwise, if the bounds are conservatively rounded across a power-of-two
  // boundary, the exponent may imply a tighter range.
  return FloorLog2(Max(Abs(r->lower()), Abs(r->upper()))) > r->exponent();
}

void Range::dump(GenericPrinter& out) const {
  assertInvariants();

  // Floating-point or Integer subset.
  if (canHaveFractionalPart_)
    out.printf("F");
  else
    out.printf("I");

  out.printf("[");

  if (!hasInt32LowerBound_)
    out.printf("?");
  else
    out.printf("%d", lower_);
  if (symbolicLower_) {
    out.printf(" {");
    symbolicLower_->dump(out);
    out.printf("}");
  }

  out.printf(", ");

  if (!hasInt32UpperBound_)
    out.printf("?");
  else
    out.printf("%d", upper_);
  if (symbolicUpper_) {
    out.printf(" {");
    symbolicUpper_->dump(out);
    out.printf("}");
  }

  out.printf("]");

  bool includesNaN = max_exponent_ == IncludesInfinityAndNaN;
  bool includesNegativeInfinity =
      max_exponent_ >= IncludesInfinity && !hasInt32LowerBound_;
  bool includesPositiveInfinity =
      max_exponent_ >= IncludesInfinity && !hasInt32UpperBound_;
  bool includesNegativeZero = canBeNegativeZero_;

  if (includesNaN || includesNegativeInfinity || includesPositiveInfinity ||
      includesNegativeZero) {
    out.printf(" (");
    bool first = true;
    if (includesNaN) {
      if (first)
        first = false;
      else
        out.printf(" ");
      out.printf("U NaN");
    }
    if (includesNegativeInfinity) {
      if (first)
        first = false;
      else
        out.printf(" ");
      out.printf("U -Infinity");
    }
    if (includesPositiveInfinity) {
      if (first)
        first = false;
      else
        out.printf(" ");
      out.printf("U Infinity");
    }
    if (includesNegativeZero) {
      if (first)
        first = false;
      else
        out.printf(" ");
      out.printf("U -0");
    }
    out.printf(")");
  }
  if (max_exponent_ < IncludesInfinity && IsExponentInteresting(this))
    out.printf(" (< pow(2, %d+1))", max_exponent_);
}

void Range::dump() const {
  Fprinter out(stderr);
  dump(out);
  out.printf("\n");
  out.finish();
}

Range* Range::intersect(TempAllocator& alloc, const Range* lhs,
                        const Range* rhs, bool* emptyRange) {
  *emptyRange = false;

  if (!lhs && !rhs) return nullptr;

  if (!lhs) return new (alloc) Range(*rhs);
  if (!rhs) return new (alloc) Range(*lhs);

  int32_t newLower = Max(lhs->lower_, rhs->lower_);
  int32_t newUpper = Min(lhs->upper_, rhs->upper_);

  // If upper < lower, then we have conflicting constraints. Consider:
  //
  // if (x < 0) {
  //   if (x > 0) {
  //     [Some code.]
  //   }
  // }
  //
  // In this case, the block is unreachable.
  if (newUpper < newLower) {
    // If both ranges can be NaN, the result can still be NaN.
    if (!lhs->canBeNaN() || !rhs->canBeNaN()) *emptyRange = true;
    return nullptr;
  }

  bool newHasInt32LowerBound =
      lhs->hasInt32LowerBound_ || rhs->hasInt32LowerBound_;
  bool newHasInt32UpperBound =
      lhs->hasInt32UpperBound_ || rhs->hasInt32UpperBound_;

  FractionalPartFlag newCanHaveFractionalPart = FractionalPartFlag(
      lhs->canHaveFractionalPart_ && rhs->canHaveFractionalPart_);
  NegativeZeroFlag newMayIncludeNegativeZero =
      NegativeZeroFlag(lhs->canBeNegativeZero_ && rhs->canBeNegativeZero_);

  uint16_t newExponent = Min(lhs->max_exponent_, rhs->max_exponent_);

  // NaN is a special value which is neither greater than infinity or less than
  // negative infinity. When we intersect two ranges like [?, 0] and [0, ?], we
  // can end up thinking we have both a lower and upper bound, even though NaN
  // is still possible. In this case, just be conservative, since any case where
  // we can have NaN is not especially interesting.
  if (newHasInt32LowerBound && newHasInt32UpperBound &&
      newExponent == IncludesInfinityAndNaN)
    return nullptr;

  // If one of the ranges has a fractional part and the other doesn't, it's
  // possible that we will have computed a newExponent that's more precise
  // than our newLower and newUpper. This is unusual, so we handle it here
  // instead of in optimize().
  //
  // For example, consider the range F[0,1.5]. Range analysis represents the
  // lower and upper bound as integers, so we'd actually have
  // F[0,2] (< pow(2, 0+1)). In this case, the exponent gives us a slightly
  // more precise upper bound than the integer upper bound.
  //
  // When intersecting such a range with an integer range, the fractional part
  // of the range is dropped. The max exponent of 0 remains valid, so the
  // upper bound needs to be adjusted to 1.
  //
  // When intersecting F[0,2] (< pow(2, 0+1)) with a range like F[2,4],
  // the naive intersection is I[2,2], but since the max exponent tells us
  // that the value is always less than 2, the intersection is actually empty.
  if (lhs->canHaveFractionalPart() != rhs->canHaveFractionalPart() ||
      (lhs->canHaveFractionalPart() && newHasInt32LowerBound &&
       newHasInt32UpperBound && newLower == newUpper)) {
    refineInt32BoundsByExponent(newExponent, &newLower, &newHasInt32LowerBound,
                                &newUpper, &newHasInt32UpperBound);

    // If we're intersecting two ranges that don't overlap, this could also
    // push the bounds past each other, since the actual intersection is
    // the empty set.
    if (newLower > newUpper) {
      *emptyRange = true;
      return nullptr;
    }
  }

  return new (alloc)
      Range(newLower, newHasInt32LowerBound, newUpper, newHasInt32UpperBound,
            newCanHaveFractionalPart, newMayIncludeNegativeZero, newExponent);
}

void Range::unionWith(const Range* other) {
  int32_t newLower = Min(lower_, other->lower_);
  int32_t newUpper = Max(upper_, other->upper_);

  bool newHasInt32LowerBound =
      hasInt32LowerBound_ && other->hasInt32LowerBound_;
  bool newHasInt32UpperBound =
      hasInt32UpperBound_ && other->hasInt32UpperBound_;

  FractionalPartFlag newCanHaveFractionalPart = FractionalPartFlag(
      canHaveFractionalPart_ || other->canHaveFractionalPart_);
  NegativeZeroFlag newMayIncludeNegativeZero =
      NegativeZeroFlag(canBeNegativeZero_ || other->canBeNegativeZero_);

  uint16_t newExponent = Max(max_exponent_, other->max_exponent_);

  rawInitialize(newLower, newHasInt32LowerBound, newUpper,
                newHasInt32UpperBound, newCanHaveFractionalPart,
                newMayIncludeNegativeZero, newExponent);
}

Range::Range(const MDefinition* def)
    : symbolicLower_(nullptr), symbolicUpper_(nullptr) {
  if (const Range* other = def->range()) {
    // The instruction has range information; use it.
    *this = *other;

    // Simulate the effect of converting the value to its type.
    // Note: we cannot clamp here, since ranges aren't allowed to shrink
    // and truncation can increase range again. So doing wrapAround to
    // mimick a possible truncation.
    switch (def->type()) {
      case MIRType::Int32:
        // MToNumberInt32 cannot truncate. So we can safely clamp.
        if (def->isToNumberInt32())
          clampToInt32();
        else
          wrapAroundToInt32();
        break;
      case MIRType::Boolean:
        wrapAroundToBoolean();
        break;
      case MIRType::None:
        MOZ_CRASH("Asking for the range of an instruction with no value");
      default:
        break;
    }
  } else {
    // Otherwise just use type information. We can trust the type here
    // because we don't care what value the instruction actually produces,
    // but what value we might get after we get past the bailouts.
    switch (def->type()) {
      case MIRType::Int32:
        setInt32(JSVAL_INT_MIN, JSVAL_INT_MAX);
        break;
      case MIRType::Boolean:
        setInt32(0, 1);
        break;
      case MIRType::None:
        MOZ_CRASH("Asking for the range of an instruction with no value");
      default:
        setUnknown();
        break;
    }
  }

  // As a special case, MUrsh is permitted to claim a result type of
  // MIRType::Int32 while actually returning values in [0,UINT32_MAX] without
  // bailouts. If range analysis hasn't ruled out values in
  // (INT32_MAX,UINT32_MAX], set the range to be conservatively correct for
  // use as either a uint32 or an int32.
  if (!hasInt32UpperBound() && def->isUrsh() &&
      def->toUrsh()->bailoutsDisabled() && def->type() != MIRType::Int64) {
    lower_ = INT32_MIN;
  }

  assertInvariants();
}

static uint16_t ExponentImpliedByDouble(double d) {
  // Handle the special values.
  if (IsNaN(d)) return Range::IncludesInfinityAndNaN;
  if (IsInfinite(d)) return Range::IncludesInfinity;

  // Otherwise take the exponent part and clamp it at zero, since the Range
  // class doesn't track fractional ranges.
  return uint16_t(Max(int_fast16_t(0), ExponentComponent(d)));
}

void Range::setDouble(double l, double h) {
  MOZ_ASSERT(!(l > h));

  // Infer lower_, upper_, hasInt32LowerBound_, and hasInt32UpperBound_.
  if (l >= INT32_MIN && l <= INT32_MAX) {
    lower_ = int32_t(::floor(l));
    hasInt32LowerBound_ = true;
  } else if (l >= INT32_MAX) {
    lower_ = INT32_MAX;
    hasInt32LowerBound_ = true;
  } else {
    lower_ = INT32_MIN;
    hasInt32LowerBound_ = false;
  }
  if (h >= INT32_MIN && h <= INT32_MAX) {
    upper_ = int32_t(::ceil(h));
    hasInt32UpperBound_ = true;
  } else if (h <= INT32_MIN) {
    upper_ = INT32_MIN;
    hasInt32UpperBound_ = true;
  } else {
    upper_ = INT32_MAX;
    hasInt32UpperBound_ = false;
  }

  // Infer max_exponent_.
  uint16_t lExp = ExponentImpliedByDouble(l);
  uint16_t hExp = ExponentImpliedByDouble(h);
  max_exponent_ = Max(lExp, hExp);

  canHaveFractionalPart_ = ExcludesFractionalParts;
  canBeNegativeZero_ = ExcludesNegativeZero;

  // Infer the canHaveFractionalPart_ setting. We can have a
  // fractional part if the range crosses through the neighborhood of zero. We
  // won't have a fractional value if the value is always beyond the point at
  // which double precision can't represent fractional values.
  uint16_t minExp = Min(lExp, hExp);
  bool includesNegative = IsNaN(l) || l < 0;
  bool includesPositive = IsNaN(h) || h > 0;
  bool crossesZero = includesNegative && includesPositive;
  if (crossesZero || minExp < MaxTruncatableExponent)
    canHaveFractionalPart_ = IncludesFractionalParts;

  // Infer the canBeNegativeZero_ setting. We can have a negative zero if
  // either bound is zero.
  if (!(l > 0) && !(h < 0)) canBeNegativeZero_ = IncludesNegativeZero;

  optimize();
}

void Range::setDoubleSingleton(double d) {
  setDouble(d, d);

  // The above setDouble call is for comparisons, and treats negative zero
  // as equal to zero. We're aiming for a minimum range, so we can clear the
  // negative zero flag if the value isn't actually negative zero.
  if (!IsNegativeZero(d)) canBeNegativeZero_ = ExcludesNegativeZero;

  assertInvariants();
}

static inline bool MissingAnyInt32Bounds(const Range* lhs, const Range* rhs) {
  return !lhs->hasInt32Bounds() || !rhs->hasInt32Bounds();
}

Range* Range::add(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  int64_t l = (int64_t)lhs->lower_ + (int64_t)rhs->lower_;
  if (!lhs->hasInt32LowerBound() || !rhs->hasInt32LowerBound())
    l = NoInt32LowerBound;

  int64_t h = (int64_t)lhs->upper_ + (int64_t)rhs->upper_;
  if (!lhs->hasInt32UpperBound() || !rhs->hasInt32UpperBound())
    h = NoInt32UpperBound;

  // The exponent is at most one greater than the greater of the operands'
  // exponents, except for NaN and infinity cases.
  uint16_t e = Max(lhs->max_exponent_, rhs->max_exponent_);
  if (e <= Range::MaxFiniteExponent) ++e;

  // Infinity + -Infinity is NaN.
  if (lhs->canBeInfiniteOrNaN() && rhs->canBeInfiniteOrNaN())
    e = Range::IncludesInfinityAndNaN;

  return new (alloc) Range(
      l, h,
      FractionalPartFlag(lhs->canHaveFractionalPart() ||
                         rhs->canHaveFractionalPart()),
      NegativeZeroFlag(lhs->canBeNegativeZero() && rhs->canBeNegativeZero()),
      e);
}

Range* Range::sub(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  int64_t l = (int64_t)lhs->lower_ - (int64_t)rhs->upper_;
  if (!lhs->hasInt32LowerBound() || !rhs->hasInt32UpperBound())
    l = NoInt32LowerBound;

  int64_t h = (int64_t)lhs->upper_ - (int64_t)rhs->lower_;
  if (!lhs->hasInt32UpperBound() || !rhs->hasInt32LowerBound())
    h = NoInt32UpperBound;

  // The exponent is at most one greater than the greater of the operands'
  // exponents, except for NaN and infinity cases.
  uint16_t e = Max(lhs->max_exponent_, rhs->max_exponent_);
  if (e <= Range::MaxFiniteExponent) ++e;

  // Infinity - Infinity is NaN.
  if (lhs->canBeInfiniteOrNaN() && rhs->canBeInfiniteOrNaN())
    e = Range::IncludesInfinityAndNaN;

  return new (alloc)
      Range(l, h,
            FractionalPartFlag(lhs->canHaveFractionalPart() ||
                               rhs->canHaveFractionalPart()),
            NegativeZeroFlag(lhs->canBeNegativeZero() && rhs->canBeZero()), e);
}

Range* Range::and_(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  MOZ_ASSERT(lhs->isInt32());
  MOZ_ASSERT(rhs->isInt32());

  // If both numbers can be negative, result can be negative in the whole range
  if (lhs->lower() < 0 && rhs->lower() < 0)
    return Range::NewInt32Range(alloc, INT32_MIN,
                                Max(lhs->upper(), rhs->upper()));

  // Only one of both numbers can be negative.
  // - result can't be negative
  // - Upper bound is minimum of both upper range,
  int32_t lower = 0;
  int32_t upper = Min(lhs->upper(), rhs->upper());

  // EXCEPT when upper bound of non negative number is max value,
  // because negative value can return the whole max value.
  // -1 & 5 = 5
  if (lhs->lower() < 0) upper = rhs->upper();
  if (rhs->lower() < 0) upper = lhs->upper();

  return Range::NewInt32Range(alloc, lower, upper);
}

Range* Range::or_(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  MOZ_ASSERT(lhs->isInt32());
  MOZ_ASSERT(rhs->isInt32());
  // When one operand is always 0 or always -1, it's a special case where we
  // can compute a fully precise result. Handling these up front also
  // protects the code below from calling CountLeadingZeroes32 with a zero
  // operand or from shifting an int32_t by 32.
  if (lhs->lower() == lhs->upper()) {
    if (lhs->lower() == 0) return new (alloc) Range(*rhs);
    if (lhs->lower() == -1) return new (alloc) Range(*lhs);
  }
  if (rhs->lower() == rhs->upper()) {
    if (rhs->lower() == 0) return new (alloc) Range(*lhs);
    if (rhs->lower() == -1) return new (alloc) Range(*rhs);
  }

  // The code below uses CountLeadingZeroes32, which has undefined behavior
  // if its operand is 0. We rely on the code above to protect it.
  MOZ_ASSERT_IF(lhs->lower() >= 0, lhs->upper() != 0);
  MOZ_ASSERT_IF(rhs->lower() >= 0, rhs->upper() != 0);
  MOZ_ASSERT_IF(lhs->upper() < 0, lhs->lower() != -1);
  MOZ_ASSERT_IF(rhs->upper() < 0, rhs->lower() != -1);

  int32_t lower = INT32_MIN;
  int32_t upper = INT32_MAX;

  if (lhs->lower() >= 0 && rhs->lower() >= 0) {
    // Both operands are non-negative, so the result won't be less than either.
    lower = Max(lhs->lower(), rhs->lower());
    // The result will have leading zeros where both operands have leading
    // zeros. CountLeadingZeroes32 of a non-negative int32 will at least be 1 to
    // account for the bit of sign.
    upper = int32_t(UINT32_MAX >> Min(CountLeadingZeroes32(lhs->upper()),
                                      CountLeadingZeroes32(rhs->upper())));
  } else {
    // The result will have leading ones where either operand has leading ones.
    if (lhs->upper() < 0) {
      unsigned leadingOnes = CountLeadingZeroes32(~lhs->lower());
      lower = Max(lower, ~int32_t(UINT32_MAX >> leadingOnes));
      upper = -1;
    }
    if (rhs->upper() < 0) {
      unsigned leadingOnes = CountLeadingZeroes32(~rhs->lower());
      lower = Max(lower, ~int32_t(UINT32_MAX >> leadingOnes));
      upper = -1;
    }
  }

  return Range::NewInt32Range(alloc, lower, upper);
}

Range* Range::xor_(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  MOZ_ASSERT(lhs->isInt32());
  MOZ_ASSERT(rhs->isInt32());
  int32_t lhsLower = lhs->lower();
  int32_t lhsUpper = lhs->upper();
  int32_t rhsLower = rhs->lower();
  int32_t rhsUpper = rhs->upper();
  bool invertAfter = false;

  // If either operand is negative, bitwise-negate it, and arrange to negate
  // the result; ~((~x)^y) == x^y. If both are negative the negations on the
  // result cancel each other out; effectively this is (~x)^(~y) == x^y.
  // These transformations reduce the number of cases we have to handle below.
  if (lhsUpper < 0) {
    lhsLower = ~lhsLower;
    lhsUpper = ~lhsUpper;
    Swap(lhsLower, lhsUpper);
    invertAfter = !invertAfter;
  }
  if (rhsUpper < 0) {
    rhsLower = ~rhsLower;
    rhsUpper = ~rhsUpper;
    Swap(rhsLower, rhsUpper);
    invertAfter = !invertAfter;
  }

  // Handle cases where lhs or rhs is always zero specially, because they're
  // easy cases where we can be perfectly precise, and because it protects the
  // CountLeadingZeroes32 calls below from seeing 0 operands, which would be
  // undefined behavior.
  int32_t lower = INT32_MIN;
  int32_t upper = INT32_MAX;
  if (lhsLower == 0 && lhsUpper == 0) {
    upper = rhsUpper;
    lower = rhsLower;
  } else if (rhsLower == 0 && rhsUpper == 0) {
    upper = lhsUpper;
    lower = lhsLower;
  } else if (lhsLower >= 0 && rhsLower >= 0) {
    // Both operands are non-negative. The result will be non-negative.
    lower = 0;
    // To compute the upper value, take each operand's upper value and
    // set all bits that don't correspond to leading zero bits in the
    // other to one. For each one, this gives an upper bound for the
    // result, so we can take the minimum between the two.
    unsigned lhsLeadingZeros = CountLeadingZeroes32(lhsUpper);
    unsigned rhsLeadingZeros = CountLeadingZeroes32(rhsUpper);
    upper = Min(rhsUpper | int32_t(UINT32_MAX >> lhsLeadingZeros),
                lhsUpper | int32_t(UINT32_MAX >> rhsLeadingZeros));
  }

  // If we bitwise-negated one (but not both) of the operands above, apply the
  // bitwise-negate to the result, completing ~((~x)^y) == x^y.
  if (invertAfter) {
    lower = ~lower;
    upper = ~upper;
    Swap(lower, upper);
  }

  return Range::NewInt32Range(alloc, lower, upper);
}

Range* Range::not_(TempAllocator& alloc, const Range* op) {
  MOZ_ASSERT(op->isInt32());
  return Range::NewInt32Range(alloc, ~op->upper(), ~op->lower());
}

Range* Range::mul(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  FractionalPartFlag newCanHaveFractionalPart = FractionalPartFlag(
      lhs->canHaveFractionalPart_ || rhs->canHaveFractionalPart_);

  NegativeZeroFlag newMayIncludeNegativeZero = NegativeZeroFlag(
      (lhs->canHaveSignBitSet() && rhs->canBeFiniteNonNegative()) ||
      (rhs->canHaveSignBitSet() && lhs->canBeFiniteNonNegative()));

  uint16_t exponent;
  if (!lhs->canBeInfiniteOrNaN() && !rhs->canBeInfiniteOrNaN()) {
    // Two finite values.
    exponent = lhs->numBits() + rhs->numBits() - 1;
    if (exponent > Range::MaxFiniteExponent) exponent = Range::IncludesInfinity;
  } else if (!lhs->canBeNaN() && !rhs->canBeNaN() &&
             !(lhs->canBeZero() && rhs->canBeInfiniteOrNaN()) &&
             !(rhs->canBeZero() && lhs->canBeInfiniteOrNaN())) {
    // Two values that multiplied together won't produce a NaN.
    exponent = Range::IncludesInfinity;
  } else {
    // Could be anything.
    exponent = Range::IncludesInfinityAndNaN;
  }

  if (MissingAnyInt32Bounds(lhs, rhs))
    return new (alloc)
        Range(NoInt32LowerBound, NoInt32UpperBound, newCanHaveFractionalPart,
              newMayIncludeNegativeZero, exponent);
  int64_t a = (int64_t)lhs->lower() * (int64_t)rhs->lower();
  int64_t b = (int64_t)lhs->lower() * (int64_t)rhs->upper();
  int64_t c = (int64_t)lhs->upper() * (int64_t)rhs->lower();
  int64_t d = (int64_t)lhs->upper() * (int64_t)rhs->upper();
  return new (alloc)
      Range(Min(Min(a, b), Min(c, d)), Max(Max(a, b), Max(c, d)),
            newCanHaveFractionalPart, newMayIncludeNegativeZero, exponent);
}

Range* Range::lsh(TempAllocator& alloc, const Range* lhs, int32_t c) {
  MOZ_ASSERT(lhs->isInt32());
  int32_t shift = c & 0x1f;

  // If the shift doesn't loose bits or shift bits into the sign bit, we
  // can simply compute the correct range by shifting.
  if ((int32_t)((uint32_t)lhs->lower() << shift << 1 >> shift >> 1) ==
          lhs->lower() &&
      (int32_t)((uint32_t)lhs->upper() << shift << 1 >> shift >> 1) ==
          lhs->upper()) {
    return Range::NewInt32Range(alloc, uint32_t(lhs->lower()) << shift,
                                uint32_t(lhs->upper()) << shift);
  }

  return Range::NewInt32Range(alloc, INT32_MIN, INT32_MAX);
}

Range* Range::rsh(TempAllocator& alloc, const Range* lhs, int32_t c) {
  MOZ_ASSERT(lhs->isInt32());
  int32_t shift = c & 0x1f;
  return Range::NewInt32Range(alloc, lhs->lower() >> shift,
                              lhs->upper() >> shift);
}

Range* Range::ursh(TempAllocator& alloc, const Range* lhs, int32_t c) {
  // ursh's left operand is uint32, not int32, but for range analysis we
  // currently approximate it as int32. We assume here that the range has
  // already been adjusted accordingly by our callers.
  MOZ_ASSERT(lhs->isInt32());

  int32_t shift = c & 0x1f;

  // If the value is always non-negative or always negative, we can simply
  // compute the correct range by shifting.
  if (lhs->isFiniteNonNegative() || lhs->isFiniteNegative()) {
    return Range::NewUInt32Range(alloc, uint32_t(lhs->lower()) >> shift,
                                 uint32_t(lhs->upper()) >> shift);
  }

  // Otherwise return the most general range after the shift.
  return Range::NewUInt32Range(alloc, 0, UINT32_MAX >> shift);
}

Range* Range::lsh(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  MOZ_ASSERT(lhs->isInt32());
  MOZ_ASSERT(rhs->isInt32());
  return Range::NewInt32Range(alloc, INT32_MIN, INT32_MAX);
}

Range* Range::rsh(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  MOZ_ASSERT(lhs->isInt32());
  MOZ_ASSERT(rhs->isInt32());

  // Canonicalize the shift range to 0 to 31.
  int32_t shiftLower = rhs->lower();
  int32_t shiftUpper = rhs->upper();
  if ((int64_t(shiftUpper) - int64_t(shiftLower)) >= 31) {
    shiftLower = 0;
    shiftUpper = 31;
  } else {
    shiftLower &= 0x1f;
    shiftUpper &= 0x1f;
    if (shiftLower > shiftUpper) {
      shiftLower = 0;
      shiftUpper = 31;
    }
  }
  MOZ_ASSERT(shiftLower >= 0 && shiftUpper <= 31);

  // The lhs bounds are signed, thus the minimum is either the lower bound
  // shift by the smallest shift if negative or the lower bound shifted by the
  // biggest shift otherwise.  And the opposite for the maximum.
  int32_t lhsLower = lhs->lower();
  int32_t min = lhsLower < 0 ? lhsLower >> shiftLower : lhsLower >> shiftUpper;
  int32_t lhsUpper = lhs->upper();
  int32_t max = lhsUpper >= 0 ? lhsUpper >> shiftLower : lhsUpper >> shiftUpper;

  return Range::NewInt32Range(alloc, min, max);
}

Range* Range::ursh(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  // ursh's left operand is uint32, not int32, but for range analysis we
  // currently approximate it as int32. We assume here that the range has
  // already been adjusted accordingly by our callers.
  MOZ_ASSERT(lhs->isInt32());
  MOZ_ASSERT(rhs->isInt32());
  return Range::NewUInt32Range(
      alloc, 0, lhs->isFiniteNonNegative() ? lhs->upper() : UINT32_MAX);
}

Range* Range::abs(TempAllocator& alloc, const Range* op) {
  int32_t l = op->lower_;
  int32_t u = op->upper_;
  FractionalPartFlag canHaveFractionalPart = op->canHaveFractionalPart_;

  // Abs never produces a negative zero.
  NegativeZeroFlag canBeNegativeZero = ExcludesNegativeZero;

  return new (alloc)
      Range(Max(Max(int32_t(0), l), u == INT32_MIN ? INT32_MAX : -u), true,
            Max(Max(int32_t(0), u), l == INT32_MIN ? INT32_MAX : -l),
            op->hasInt32Bounds() && l != INT32_MIN, canHaveFractionalPart,
            canBeNegativeZero, op->max_exponent_);
}

Range* Range::min(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  // If either operand is NaN, the result is NaN.
  if (lhs->canBeNaN() || rhs->canBeNaN()) return nullptr;

  FractionalPartFlag newCanHaveFractionalPart = FractionalPartFlag(
      lhs->canHaveFractionalPart_ || rhs->canHaveFractionalPart_);
  NegativeZeroFlag newMayIncludeNegativeZero =
      NegativeZeroFlag(lhs->canBeNegativeZero_ || rhs->canBeNegativeZero_);

  return new (alloc) Range(Min(lhs->lower_, rhs->lower_),
                           lhs->hasInt32LowerBound_ && rhs->hasInt32LowerBound_,
                           Min(lhs->upper_, rhs->upper_),
                           lhs->hasInt32UpperBound_ || rhs->hasInt32UpperBound_,
                           newCanHaveFractionalPart, newMayIncludeNegativeZero,
                           Max(lhs->max_exponent_, rhs->max_exponent_));
}

Range* Range::max(TempAllocator& alloc, const Range* lhs, const Range* rhs) {
  // If either operand is NaN, the result is NaN.
  if (lhs->canBeNaN() || rhs->canBeNaN()) return nullptr;

  FractionalPartFlag newCanHaveFractionalPart = FractionalPartFlag(
      lhs->canHaveFractionalPart_ || rhs->canHaveFractionalPart_);
  NegativeZeroFlag newMayIncludeNegativeZero =
      NegativeZeroFlag(lhs->canBeNegativeZero_ || rhs->canBeNegativeZero_);

  return new (alloc) Range(Max(lhs->lower_, rhs->lower_),
                           lhs->hasInt32LowerBound_ || rhs->hasInt32LowerBound_,
                           Max(lhs->upper_, rhs->upper_),
                           lhs->hasInt32UpperBound_ && rhs->hasInt32UpperBound_,
                           newCanHaveFractionalPart, newMayIncludeNegativeZero,
                           Max(lhs->max_exponent_, rhs->max_exponent_));
}

Range* Range::floor(TempAllocator& alloc, const Range* op) {
  Range* copy = new (alloc) Range(*op);
  // Decrement lower bound of copy range if op have a factional part and lower
  // bound is Int32 defined. Also we avoid to decrement when op have a
  // fractional part but lower_ >= JSVAL_INT_MAX.
  if (op->canHaveFractionalPart() && op->hasInt32LowerBound())
    copy->setLowerInit(int64_t(copy->lower_) - 1);

  // Also refine max_exponent_ because floor may have decremented int value
  // If we've got int32 defined bounds, just deduce it using defined bounds.
  // But, if we don't have those, value's max_exponent_ may have changed.
  // Because we're looking to maintain an over estimation, if we can,
  // we increment it.
  if (copy->hasInt32Bounds())
    copy->max_exponent_ = copy->exponentImpliedByInt32Bounds();
  else if (copy->max_exponent_ < MaxFiniteExponent)
    copy->max_exponent_++;

  copy->canHaveFractionalPart_ = ExcludesFractionalParts;
  copy->assertInvariants();
  return copy;
}

Range* Range::ceil(TempAllocator& alloc, const Range* op) {
  Range* copy = new (alloc) Range(*op);

  // We need to refine max_exponent_ because ceil may have incremented the int
  // value. If we have got int32 bounds defined, just deduce it using the
  // defined bounds. Else we can just increment its value, as we are looking to
  // maintain an over estimation.
  if (copy->hasInt32Bounds())
    copy->max_exponent_ = copy->exponentImpliedByInt32Bounds();
  else if (copy->max_exponent_ < MaxFiniteExponent)
    copy->max_exponent_++;

  copy->canHaveFractionalPart_ = ExcludesFractionalParts;
  copy->assertInvariants();
  return copy;
}

Range* Range::sign(TempAllocator& alloc, const Range* op) {
  if (op->canBeNaN()) return nullptr;

  return new (alloc)
      Range(Max(Min(op->lower_, 1), -1), Max(Min(op->upper_, 1), -1),
            Range::ExcludesFractionalParts,
            NegativeZeroFlag(op->canBeNegativeZero()), 0);
}

Range* Range::NaNToZero(TempAllocator& alloc, const Range* op) {
  Range* copy = new (alloc) Range(*op);
  if (copy->canBeNaN()) {
    copy->max_exponent_ = Range::IncludesInfinity;
    if (!copy->canBeZero()) {
      Range zero;
      zero.setDoubleSingleton(0);
      copy->unionWith(&zero);
    }
  }
  copy->refineToExcludeNegativeZero();
  return copy;
}

bool Range::negativeZeroMul(const Range* lhs, const Range* rhs) {
  // The result can only be negative zero if both sides are finite and they
  // have differing signs.
  return (lhs->canHaveSignBitSet() && rhs->canBeFiniteNonNegative()) ||
         (rhs->canHaveSignBitSet() && lhs->canBeFiniteNonNegative());
}

bool Range::update(const Range* other) {
  bool changed = lower_ != other->lower_ ||
                 hasInt32LowerBound_ != other->hasInt32LowerBound_ ||
                 upper_ != other->upper_ ||
                 hasInt32UpperBound_ != other->hasInt32UpperBound_ ||
                 canHaveFractionalPart_ != other->canHaveFractionalPart_ ||
                 canBeNegativeZero_ != other->canBeNegativeZero_ ||
                 max_exponent_ != other->max_exponent_;
  if (changed) {
    lower_ = other->lower_;
    hasInt32LowerBound_ = other->hasInt32LowerBound_;
    upper_ = other->upper_;
    hasInt32UpperBound_ = other->hasInt32UpperBound_;
    canHaveFractionalPart_ = other->canHaveFractionalPart_;
    canBeNegativeZero_ = other->canBeNegativeZero_;
    max_exponent_ = other->max_exponent_;
    assertInvariants();
  }

  return changed;
}

///////////////////////////////////////////////////////////////////////////////
// Range Computation for MIR Nodes
///////////////////////////////////////////////////////////////////////////////

void MPhi::computeRange(TempAllocator& alloc) {
  if (type() != MIRType::Int32 && type() != MIRType::Double) return;

  Range* range = nullptr;
  for (size_t i = 0, e = numOperands(); i < e; i++) {
    if (getOperand(i)->block()->unreachable()) {
      JitSpew(JitSpew_Range, "Ignoring unreachable input %d",
              getOperand(i)->id());
      continue;
    }

    // Peek at the pre-bailout range so we can take a short-cut; if any of
    // the operands has an unknown range, this phi has an unknown range.
    if (!getOperand(i)->range()) return;

    Range input(getOperand(i));

    if (range)
      range->unionWith(&input);
    else
      range = new (alloc) Range(input);
  }

  setRange(range);
}

void MBeta::computeRange(TempAllocator& alloc) {
  bool emptyRange = false;

  Range opRange(getOperand(0));
  Range* range = Range::intersect(alloc, &opRange, comparison_, &emptyRange);
  if (emptyRange) {
    JitSpew(JitSpew_Range, "Marking block for inst %d unreachable", id());
    block()->setUnreachableUnchecked();
  } else {
    setRange(range);
  }
}

void MConstant::computeRange(TempAllocator& alloc) {
  if (isTypeRepresentableAsDouble()) {
    double d = numberToDouble();
    setRange(Range::NewDoubleSingletonRange(alloc, d));
  } else if (type() == MIRType::Boolean) {
    bool b = toBoolean();
    setRange(Range::NewInt32Range(alloc, b, b));
  }
}

void MCharCodeAt::computeRange(TempAllocator& alloc) {
  // ECMA 262 says that the integer will be non-negative and at most 65535.
  setRange(Range::NewInt32Range(alloc, 0, 65535));
}

void MClampToUint8::computeRange(TempAllocator& alloc) {
  setRange(Range::NewUInt32Range(alloc, 0, 255));
}

void MBitAnd::computeRange(TempAllocator& alloc) {
  if (specialization_ == MIRType::Int64) return;

  Range left(getOperand(0));
  Range right(getOperand(1));
  left.wrapAroundToInt32();
  right.wrapAroundToInt32();

  setRange(Range::and_(alloc, &left, &right));
}

void MBitOr::computeRange(TempAllocator& alloc) {
  if (specialization_ == MIRType::Int64) return;

  Range left(getOperand(0));
  Range right(getOperand(1));
  left.wrapAroundToInt32();
  right.wrapAroundToInt32();

  setRange(Range::or_(alloc, &left, &right));
}

void MBitXor::computeRange(TempAllocator& alloc) {
  if (specialization_ == MIRType::Int64) return;

  Range left(getOperand(0));
  Range right(getOperand(1));
  left.wrapAroundToInt32();
  right.wrapAroundToInt32();

  setRange(Range::xor_(alloc, &left, &right));
}

void MBitNot::computeRange(TempAllocator& alloc) {
  Range op(getOperand(0));
  op.wrapAroundToInt32();

  setRange(Range::not_(alloc, &op));
}

void MLsh::computeRange(TempAllocator& alloc) {
  if (specialization_ == MIRType::Int64) return;

  Range left(getOperand(0));
  Range right(getOperand(1));
  left.wrapAroundToInt32();

  MConstant* rhsConst = getOperand(1)->maybeConstantValue();
  if (rhsConst && rhsConst->type() == MIRType::Int32) {
    int32_t c = rhsConst->toInt32();
    setRange(Range::lsh(alloc, &left, c));
    return;
  }

  right.wrapAroundToShiftCount();
  setRange(Range::lsh(alloc, &left, &right));
}

void MRsh::computeRange(TempAllocator& alloc) {
  if (specialization_ == MIRType::Int64) return;

  Range left(getOperand(0));
  Range right(getOperand(1));
  left.wrapAroundToInt32();

  MConstant* rhsConst = getOperand(1)->maybeConstantValue();
  if (rhsConst && rhsConst->type() == MIRType::Int32) {
    int32_t c = rhsConst->toInt32();
    setRange(Range::rsh(alloc, &left, c));
    return;
  }

  right.wrapAroundToShiftCount();
  setRange(Range::rsh(alloc, &left, &right));
}

void MUrsh::computeRange(TempAllocator& alloc) {
  if (specialization_ == MIRType::Int64) return;

  Range left(getOperand(0));
  Range right(getOperand(1));

  // ursh can be thought of as converting its left operand to uint32, or it
  // can be thought of as converting its left operand to int32, and then
  // reinterpreting the int32 bits as a uint32 value. Both approaches yield
  // the same result. Since we lack support for full uint32 ranges, we use
  // the second interpretation, though it does cause us to be conservative.
  left.wrapAroundToInt32();
  right.wrapAroundToShiftCount();

  MConstant* rhsConst = getOperand(1)->maybeConstantValue();
  if (rhsConst && rhsConst->type() == MIRType::Int32) {
    int32_t c = rhsConst->toInt32();
    setRange(Range::ursh(alloc, &left, c));
  } else {
    setRange(Range::ursh(alloc, &left, &right));
  }

  MOZ_ASSERT(range()->lower() >= 0);
}

void MAbs::computeRange(TempAllocator& alloc) {
  if (specialization_ != MIRType::Int32 && specialization_ != MIRType::Double)
    return;

  Range other(getOperand(0));
  Range* next = Range::abs(alloc, &other);
  if (implicitTruncate_) next->wrapAroundToInt32();
  setRange(next);
}

void MFloor::computeRange(TempAllocator& alloc) {
  Range other(getOperand(0));
  setRange(Range::floor(alloc, &other));
}

void MCeil::computeRange(TempAllocator& alloc) {
  Range other(getOperand(0));
  setRange(Range::ceil(alloc, &other));
}

void MClz::computeRange(TempAllocator& alloc) {
  if (type() != MIRType::Int32) return;
  setRange(Range::NewUInt32Range(alloc, 0, 32));
}

void MCtz::computeRange(TempAllocator& alloc) {
  if (type() != MIRType::Int32) return;
  setRange(Range::NewUInt32Range(alloc, 0, 32));
}

void MPopcnt::computeRange(TempAllocator& alloc) {
  if (type() != MIRType::Int32) return;
  setRange(Range::NewUInt32Range(alloc, 0, 32));
}

void MMinMax::computeRange(TempAllocator& alloc) {
  if (specialization_ != MIRType::Int32 && specialization_ != MIRType::Double)
    return;

  Range left(getOperand(0));
  Range right(getOperand(1));
  setRange(isMax() ? Range::max(alloc, &left, &right)
                   : Range::min(alloc, &left, &right));
}

void MAdd::computeRange(TempAllocator& alloc) {
  if (specialization() != MIRType::Int32 && specialization() != MIRType::Double)
    return;
  Range left(getOperand(0));
  Range right(getOperand(1));
  Range* next = Range::add(alloc, &left, &right);
  if (isTruncated()) next->wrapAroundToInt32();
  setRange(next);
}

void MSub::computeRange(TempAllocator& alloc) {
  if (specialization() != MIRType::Int32 && specialization() != MIRType::Double)
    return;
  Range left(getOperand(0));
  Range right(getOperand(1));
  Range* next = Range::sub(alloc, &left, &right);
  if (isTruncated()) next->wrapAroundToInt32();
  setRange(next);
}

void MMul::computeRange(TempAllocator& alloc) {
  if (specialization() != MIRType::Int32 && specialization() != MIRType::Double)
    return;
  Range left(getOperand(0));
  Range right(getOperand(1));
  if (canBeNegativeZero())
    canBeNegativeZero_ = Range::negativeZeroMul(&left, &right);
  Range* next = Range::mul(alloc, &left, &right);
  if (!next->canBeNegativeZero()) canBeNegativeZero_ = false;
  // Truncated multiplications could overflow in both directions
  if (isTruncated()) next->wrapAroundToInt32();
  setRange(next);
}

void MMod::computeRange(TempAllocator& alloc) {
  if (specialization() != MIRType::Int32 && specialization() != MIRType::Double)
    return;
  Range lhs(getOperand(0));
  Range rhs(getOperand(1));

  // If either operand is a NaN, the result is NaN. This also conservatively
  // handles Infinity cases.
  if (!lhs.hasInt32Bounds() || !rhs.hasInt32Bounds()) return;

  // If RHS can be zero, the result can be NaN.
  if (rhs.lower() <= 0 && rhs.upper() >= 0) return;

  // If both operands are non-negative integers, we can optimize this to an
  // unsigned mod.
  if (specialization() == MIRType::Int32 && rhs.lower() > 0) {
    bool hasDoubles = lhs.lower() < 0 || lhs.canHaveFractionalPart() ||
                      rhs.canHaveFractionalPart();
    // It is not possible to check that lhs.lower() >= 0, since the range
    // of a ursh with rhs a 0 constant is wrapped around the int32 range in
    // Range::Range(). However, IsUint32Type() will only return true for
    // nodes that lie in the range [0, UINT32_MAX].
    bool hasUint32s =
        IsUint32Type(getOperand(0)) &&
        getOperand(1)->type() == MIRType::Int32 &&
        (IsUint32Type(getOperand(1)) || getOperand(1)->isConstant());
    if (!hasDoubles || hasUint32s) unsigned_ = true;
  }

  // For unsigned mod, we have to convert both operands to unsigned.
  // Note that we handled the case of a zero rhs above.
  if (unsigned_) {
    // The result of an unsigned mod will never be unsigned-greater than
    // either operand.
    uint32_t lhsBound = Max<uint32_t>(lhs.lower(), lhs.upper());
    uint32_t rhsBound = Max<uint32_t>(rhs.lower(), rhs.upper());

    // If either range crosses through -1 as a signed value, it could be
    // the maximum unsigned value when interpreted as unsigned. If the range
    // doesn't include -1, then the simple max value we computed above is
    // correct.
    if (lhs.lower() <= -1 && lhs.upper() >= -1) lhsBound = UINT32_MAX;
    if (rhs.lower() <= -1 && rhs.upper() >= -1) rhsBound = UINT32_MAX;

    // The result will never be equal to the rhs, and we shouldn't have
    // any rounding to worry about.
    MOZ_ASSERT(!lhs.canHaveFractionalPart() && !rhs.canHaveFractionalPart());
    --rhsBound;

    // This gives us two upper bounds, so we can take the best one.
    setRange(Range::NewUInt32Range(alloc, 0, Min(lhsBound, rhsBound)));
    return;
  }

  // Math.abs(lhs % rhs) == Math.abs(lhs) % Math.abs(rhs).
  // First, the absolute value of the result will always be less than the
  // absolute value of rhs. (And if rhs is zero, the result is NaN).
  int64_t a = Abs<int64_t>(rhs.lower());
  int64_t b = Abs<int64_t>(rhs.upper());
  if (a == 0 && b == 0) return;
  int64_t rhsAbsBound = Max(a, b);

  // If the value is known to be integer, less-than abs(rhs) is equivalent
  // to less-than-or-equal abs(rhs)-1. This is important for being able to
  // say that the result of x%256 is an 8-bit unsigned number.
  if (!lhs.canHaveFractionalPart() && !rhs.canHaveFractionalPart())
    --rhsAbsBound;

  // Next, the absolute value of the result will never be greater than the
  // absolute value of lhs.
  int64_t lhsAbsBound =
      Max(Abs<int64_t>(lhs.lower()), Abs<int64_t>(lhs.upper()));

  // This gives us two upper bounds, so we can take the best one.
  int64_t absBound = Min(lhsAbsBound, rhsAbsBound);

  // Now consider the sign of the result.
  // If lhs is non-negative, the result will be non-negative.
  // If lhs is non-positive, the result will be non-positive.
  int64_t lower = lhs.lower() >= 0 ? 0 : -absBound;
  int64_t upper = lhs.upper() <= 0 ? 0 : absBound;

  Range::FractionalPartFlag newCanHaveFractionalPart =
      Range::FractionalPartFlag(lhs.canHaveFractionalPart() ||
                                rhs.canHaveFractionalPart());

  // If the lhs can have the sign bit set and we can return a zero, it'll be a
  // negative zero.
  Range::NegativeZeroFlag newMayIncludeNegativeZero =
      Range::NegativeZeroFlag(lhs.canHaveSignBitSet());

  setRange(new (alloc) Range(lower, upper, newCanHaveFractionalPart,
                             newMayIncludeNegativeZero,
                             Min(lhs.exponent(), rhs.exponent())));
}

void MDiv::computeRange(TempAllocator& alloc) {
  if (specialization() != MIRType::Int32 && specialization() != MIRType::Double)
    return;
  Range lhs(getOperand(0));
  Range rhs(getOperand(1));

  // If either operand is a NaN, the result is NaN. This also conservatively
  // handles Infinity cases.
  if (!lhs.hasInt32Bounds() || !rhs.hasInt32Bounds()) return;

  // Something simple for now: When dividing by a positive rhs, the result
  // won't be further from zero than lhs.
  if (lhs.lower() >= 0 && rhs.lower() >= 1) {
    setRange(new (alloc) Range(0, lhs.upper(), Range::IncludesFractionalParts,
                               Range::IncludesNegativeZero, lhs.exponent()));
  } else if (unsigned_ && rhs.lower() >= 1) {
    // We shouldn't set the unsigned flag if the inputs can have
    // fractional parts.
    MOZ_ASSERT(!lhs.canHaveFractionalPart() && !rhs.canHaveFractionalPart());
    // We shouldn't set the unsigned flag if the inputs can be
    // negative zero.
    MOZ_ASSERT(!lhs.canBeNegativeZero() && !rhs.canBeNegativeZero());
    // Unsigned division by a non-zero rhs will return a uint32 value.
    setRange(Range::NewUInt32Range(alloc, 0, UINT32_MAX));
  }
}

void MSqrt::computeRange(TempAllocator& alloc) {
  Range input(getOperand(0));

  // If either operand is a NaN, the result is NaN. This also conservatively
  // handles Infinity cases.
  if (!input.hasInt32Bounds()) return;

  // Sqrt of a negative non-zero value is NaN.
  if (input.lower() < 0) return;

  // Something simple for now: When taking the sqrt of a positive value, the
  // result won't be further from zero than the input.
  // And, sqrt of an integer may have a fractional part.
  setRange(new (alloc) Range(0, input.upper(), Range::IncludesFractionalParts,
                             input.canBeNegativeZero(), input.exponent()));
}

void MToDouble::computeRange(TempAllocator& alloc) {
  setRange(new (alloc) Range(getOperand(0)));
}

void MToFloat32::computeRange(TempAllocator& alloc) {}

void MTruncateToInt32::computeRange(TempAllocator& alloc) {
  Range* output = new (alloc) Range(getOperand(0));
  output->wrapAroundToInt32();
  setRange(output);
}

void MToNumberInt32::computeRange(TempAllocator& alloc) {
  // No clamping since this computes the range *before* bailouts.
  setRange(new (alloc) Range(getOperand(0)));
}

void MLimitedTruncate::computeRange(TempAllocator& alloc) {
  Range* output = new (alloc) Range(input());
  setRange(output);
}

void MFilterTypeSet::computeRange(TempAllocator& alloc) {
  setRange(new (alloc) Range(getOperand(0)));
}

static Range* GetTypedArrayRange(TempAllocator& alloc, Scalar::Type type) {
  switch (type) {
    case Scalar::Uint8Clamped:
    case Scalar::Uint8:
      return Range::NewUInt32Range(alloc, 0, UINT8_MAX);
    case Scalar::Uint16:
      return Range::NewUInt32Range(alloc, 0, UINT16_MAX);
    case Scalar::Uint32:
      return Range::NewUInt32Range(alloc, 0, UINT32_MAX);

    case Scalar::Int8:
      return Range::NewInt32Range(alloc, INT8_MIN, INT8_MAX);
    case Scalar::Int16:
      return Range::NewInt32Range(alloc, INT16_MIN, INT16_MAX);
    case Scalar::Int32:
      return Range::NewInt32Range(alloc, INT32_MIN, INT32_MAX);

    case Scalar::Int64:
    case Scalar::Float32:
    case Scalar::Float64:
    case Scalar::Float32x4:
    case Scalar::Int8x16:
    case Scalar::Int16x8:
    case Scalar::Int32x4:
    case Scalar::MaxTypedArrayViewType:
      break;
  }
  return nullptr;
}

void MLoadUnboxedScalar::computeRange(TempAllocator& alloc) {
  // We have an Int32 type and if this is a UInt32 load it may produce a value
  // outside of our range, but we have a bailout to handle those cases.
  setRange(GetTypedArrayRange(alloc, readType()));
}

void MArrayLength::computeRange(TempAllocator& alloc) {
  // Array lengths can go up to UINT32_MAX, but we only create MArrayLength
  // nodes when the value is known to be int32 (see the
  // OBJECT_FLAG_LENGTH_OVERFLOW flag).
  setRange(Range::NewUInt32Range(alloc, 0, INT32_MAX));
}

void MInitializedLength::computeRange(TempAllocator& alloc) {
  setRange(
      Range::NewUInt32Range(alloc, 0, NativeObject::MAX_DENSE_ELEMENTS_COUNT));
}

void MTypedArrayLength::computeRange(TempAllocator& alloc) {
  setRange(Range::NewUInt32Range(alloc, 0, INT32_MAX));
}

void MStringLength::computeRange(TempAllocator& alloc) {
  static_assert(JSString::MAX_LENGTH <= UINT32_MAX,
                "NewUInt32Range requires a uint32 value");
  setRange(Range::NewUInt32Range(alloc, 0, JSString::MAX_LENGTH));
}

void MArgumentsLength::computeRange(TempAllocator& alloc) {
  // This is is a conservative upper bound on what |TooManyActualArguments|
  // checks.  If exceeded, Ion will not be entered in the first place.
  static_assert(ARGS_LENGTH_MAX <= UINT32_MAX,
                "NewUInt32Range requires a uint32 value");
  setRange(Range::NewUInt32Range(alloc, 0, ARGS_LENGTH_MAX));
}

void MBoundsCheck::computeRange(TempAllocator& alloc) {
  // Just transfer the incoming index range to the output. The length() is
  // also interesting, but it is handled as a bailout check, and we're
  // computing a pre-bailout range here.
  setRange(new (alloc) Range(index()));
}

void MSpectreMaskIndex::computeRange(TempAllocator& alloc) {
  // Just transfer the incoming index range to the output for now.
  setRange(new (alloc) Range(index()));
}

void MArrayPush::computeRange(TempAllocator& alloc) {
  // MArrayPush returns the new array length.
  setRange(Range::NewUInt32Range(alloc, 0, UINT32_MAX));
}

void MMathFunction::computeRange(TempAllocator& alloc) {
  Range opRange(getOperand(0));
  switch (function()) {
    case Sin:
    case Cos:
      if (!opRange.canBeInfiniteOrNaN())
        setRange(Range::NewDoubleRange(alloc, -1.0, 1.0));
      break;
    case Sign:
      setRange(Range::sign(alloc, &opRange));
      break;
    default:
      break;
  }
}

void MRandom::computeRange(TempAllocator& alloc) {
  Range* r = Range::NewDoubleRange(alloc, 0.0, 1.0);

  // Random never returns negative zero.
  r->refineToExcludeNegativeZero();

  setRange(r);
}

void MNaNToZero::computeRange(TempAllocator& alloc) {
  Range other(input());
  setRange(Range::NaNToZero(alloc, &other));
}

///////////////////////////////////////////////////////////////////////////////
// Range Analysis
///////////////////////////////////////////////////////////////////////////////

bool RangeAnalysis::analyzeLoop(MBasicBlock* header) {
  MOZ_ASSERT(header->hasUniqueBackedge());

  // Try to compute an upper bound on the number of times the loop backedge
  // will be taken. Look for tests that dominate the backedge and which have
  // an edge leaving the loop body.
  MBasicBlock* backedge = header->backedge();

  // Ignore trivial infinite loops.
  if (backedge == header) return true;

  bool canOsr;
  size_t numBlocks = MarkLoopBlocks(graph_, header, &canOsr);

  // Ignore broken loops.
  if (numBlocks == 0) return true;

  LoopIterationBound* iterationBound = nullptr;

  MBasicBlock* block = backedge;
  do {
    BranchDirection direction;
    MTest* branch = block->immediateDominatorBranch(&direction);

    if (block == block->immediateDominator()) break;

    block = block->immediateDominator();

    if (branch) {
      direction = NegateBranchDirection(direction);
      MBasicBlock* otherBlock = branch->branchSuccessor(direction);
      if (!otherBlock->isMarked()) {
        if (!alloc().ensureBallast()) return false;
        iterationBound = analyzeLoopIterationCount(header, branch, direction);
        if (iterationBound) break;
      }
    }
  } while (block != header);

  if (!iterationBound) {
    UnmarkLoopBlocks(graph_, header);
    return true;
  }

  if (!loopIterationBounds.append(iterationBound)) return false;

#ifdef DEBUG
  if (JitSpewEnabled(JitSpew_Range)) {
    Sprinter sp(GetJitContext()->cx);
    if (!sp.init()) return false;
    iterationBound->boundSum.dump(sp);
    JitSpew(JitSpew_Range, "computed symbolic bound on backedges: %s",
            sp.string());
  }
#endif

  // Try to compute symbolic bounds for the phi nodes at the head of this
  // loop, expressed in terms of the iteration bound just computed.

  for (MPhiIterator iter(header->phisBegin()); iter != header->phisEnd();
       iter++)
    analyzeLoopPhi(iterationBound, *iter);

  if (!mir->compilingWasm()) {
    // Try to hoist any bounds checks from the loop using symbolic bounds.

    Vector<MBoundsCheck*, 0, JitAllocPolicy> hoistedChecks(alloc());

    for (ReversePostorderIterator iter(graph_.rpoBegin(header));
         iter != graph_.rpoEnd(); iter++) {
      MBasicBlock* block = *iter;
      if (!block->isMarked()) continue;

      for (MDefinitionIterator iter(block); iter; iter++) {
        MDefinition* def = *iter;
        if (def->isBoundsCheck() && def->isMovable()) {
          if (!alloc().ensureBallast()) return false;
          if (tryHoistBoundsCheck(header, def->toBoundsCheck())) {
            if (!hoistedChecks.append(def->toBoundsCheck())) return false;
          }
        }
      }
    }

    // Note: replace all uses of the original bounds check with the
    // actual index. This is usually done during bounds check elimination,
    // but in this case it's safe to do it here since the load/store is
    // definitely not loop-invariant, so we will never move it before
    // one of the bounds checks we just added.
    for (size_t i = 0; i < hoistedChecks.length(); i++) {
      MBoundsCheck* ins = hoistedChecks[i];
      ins->replaceAllUsesWith(ins->index());
      ins->block()->discard(ins);
    }
  }

  UnmarkLoopBlocks(graph_, header);
  return true;
}

// Unbox beta nodes in order to hoist instruction properly, and not be limited
// by the beta nodes which are added after each branch.
static inline MDefinition* DefinitionOrBetaInputDefinition(MDefinition* ins) {
  while (ins->isBeta()) ins = ins->toBeta()->input();
  return ins;
}

LoopIterationBound* RangeAnalysis::analyzeLoopIterationCount(
    MBasicBlock* header, MTest* test, BranchDirection direction) {
  SimpleLinearSum lhs(nullptr, 0);
  MDefinition* rhs;
  bool lessEqual;
  if (!ExtractLinearInequality(test, direction, &lhs, &rhs, &lessEqual))
    return nullptr;

  // Ensure the rhs is a loop invariant term.
  if (rhs && rhs->block()->isMarked()) {
    if (lhs.term && lhs.term->block()->isMarked()) return nullptr;
    MDefinition* temp = lhs.term;
    lhs.term = rhs;
    rhs = temp;
    if (!SafeSub(0, lhs.constant, &lhs.constant)) return nullptr;
    lessEqual = !lessEqual;
  }

  MOZ_ASSERT_IF(rhs, !rhs->block()->isMarked());

  // Ensure the lhs is a phi node from the start of the loop body.
  if (!lhs.term || !lhs.term->isPhi() || lhs.term->block() != header)
    return nullptr;

  // Check that the value of the lhs changes by a constant amount with each
  // loop iteration. This requires that the lhs be written in every loop
  // iteration with a value that is a constant difference from its value at
  // the start of the iteration.

  if (lhs.term->toPhi()->numOperands() != 2) return nullptr;

  // The first operand of the phi should be the lhs' value at the start of
  // the first executed iteration, and not a value written which could
  // replace the second operand below during the middle of execution.
  MDefinition* lhsInitial = lhs.term->toPhi()->getLoopPredecessorOperand();
  if (lhsInitial->block()->isMarked()) return nullptr;

  // The second operand of the phi should be a value written by an add/sub
  // in every loop iteration, i.e. in a block which dominates the backedge.
  MDefinition* lhsWrite = DefinitionOrBetaInputDefinition(
      lhs.term->toPhi()->getLoopBackedgeOperand());
  if (!lhsWrite->isAdd() && !lhsWrite->isSub()) return nullptr;
  if (!lhsWrite->block()->isMarked()) return nullptr;
  MBasicBlock* bb = header->backedge();
  for (; bb != lhsWrite->block() && bb != header;
       bb = bb->immediateDominator()) {
  }
  if (bb != lhsWrite->block()) return nullptr;

  SimpleLinearSum lhsModified = ExtractLinearSum(lhsWrite);

  // Check that the value of the lhs at the backedge is of the form
  // 'old(lhs) + N'. We can be sure that old(lhs) is the value at the start
  // of the iteration, and not that written to lhs in a previous iteration,
  // as such a previous value could not appear directly in the addition:
  // it could not be stored in lhs as the lhs add/sub executes in every
  // iteration, and if it were stored in another variable its use here would
  // be as an operand to a phi node for that variable.
  if (lhsModified.term != lhs.term) return nullptr;

  LinearSum iterationBound(alloc());
  LinearSum currentIteration(alloc());

  if (lhsModified.constant == 1 && !lessEqual) {
    // The value of lhs is 'initial(lhs) + iterCount' and this will end
    // execution of the loop if 'lhs + lhsN >= rhs'. Thus, an upper bound
    // on the number of backedges executed is:
    //
    // initial(lhs) + iterCount + lhsN == rhs
    // iterCount == rhsN - initial(lhs) - lhsN

    if (rhs) {
      if (!iterationBound.add(rhs, 1)) return nullptr;
    }
    if (!iterationBound.add(lhsInitial, -1)) return nullptr;

    int32_t lhsConstant;
    if (!SafeSub(0, lhs.constant, &lhsConstant)) return nullptr;
    if (!iterationBound.add(lhsConstant)) return nullptr;

    if (!currentIteration.add(lhs.term, 1)) return nullptr;
    if (!currentIteration.add(lhsInitial, -1)) return nullptr;
  } else if (lhsModified.constant == -1 && lessEqual) {
    // The value of lhs is 'initial(lhs) - iterCount'. Similar to the above
    // case, an upper bound on the number of backedges executed is:
    //
    // initial(lhs) - iterCount + lhsN == rhs
    // iterCount == initial(lhs) - rhs + lhsN

    if (!iterationBound.add(lhsInitial, 1)) return nullptr;
    if (rhs) {
      if (!iterationBound.add(rhs, -1)) return nullptr;
    }
    if (!iterationBound.add(lhs.constant)) return nullptr;

    if (!currentIteration.add(lhsInitial, 1)) return nullptr;
    if (!currentIteration.add(lhs.term, -1)) return nullptr;
  } else {
    return nullptr;
  }

  return new (alloc())
      LoopIterationBound(header, test, iterationBound, currentIteration);
}

void RangeAnalysis::analyzeLoopPhi(LoopIterationBound* loopBound, MPhi* phi) {
  // Given a bound on the number of backedges taken, compute an upper and
  // lower bound for a phi node that may change by a constant amount each
  // iteration. Unlike for the case when computing the iteration bound
  // itself, the phi does not need to change the same amount every iteration,
  // but is required to change at most N and be either nondecreasing or
  // nonincreasing.

  MOZ_ASSERT(phi->numOperands() == 2);

  MDefinition* initial = phi->getLoopPredecessorOperand();
  if (initial->block()->isMarked()) return;

  SimpleLinearSum modified =
      ExtractLinearSum(phi->getLoopBackedgeOperand(), MathSpace::Infinite);

  if (modified.term != phi || modified.constant == 0) return;

  if (!phi->range()) phi->setRange(new (alloc()) Range(phi));

  LinearSum initialSum(alloc());
  if (!initialSum.add(initial, 1)) return;

  // The phi may change by N each iteration, and is either nondecreasing or
  // nonincreasing. initial(phi) is either a lower or upper bound for the
  // phi, and initial(phi) + loopBound * N is either an upper or lower bound,
  // at all points within the loop, provided that loopBound >= 0.
  //
  // We are more interested, however, in the bound for phi at points
  // dominated by the loop bound's test; if the test dominates e.g. a bounds
  // check we want to hoist from the loop, using the value of the phi at the
  // head of the loop for this will usually be too imprecise to hoist the
  // check. These points will execute only if the backedge executes at least
  // one more time (as the test passed and the test dominates the backedge),
  // so we know both that loopBound >= 1 and that the phi's value has changed
  // at most loopBound - 1 times. Thus, another upper or lower bound for the
  // phi is initial(phi) + (loopBound - 1) * N, without requiring us to
  // ensure that loopBound >= 0.

  LinearSum limitSum(loopBound->boundSum);
  if (!limitSum.multiply(modified.constant) || !limitSum.add(initialSum))
    return;

  int32_t negativeConstant;
  if (!SafeSub(0, modified.constant, &negativeConstant) ||
      !limitSum.add(negativeConstant))
    return;

  Range* initRange = initial->range();
  if (modified.constant > 0) {
    if (initRange && initRange->hasInt32LowerBound())
      phi->range()->refineLower(initRange->lower());
    phi->range()->setSymbolicLower(
        SymbolicBound::New(alloc(), nullptr, initialSum));
    phi->range()->setSymbolicUpper(
        SymbolicBound::New(alloc(), loopBound, limitSum));
  } else {
    if (initRange && initRange->hasInt32UpperBound())
      phi->range()->refineUpper(initRange->upper());
    phi->range()->setSymbolicUpper(
        SymbolicBound::New(alloc(), nullptr, initialSum));
    phi->range()->setSymbolicLower(
        SymbolicBound::New(alloc(), loopBound, limitSum));
  }

  JitSpew(JitSpew_Range, "added symbolic range on %d", phi->id());
  SpewRange(phi);
}

// Whether bound is valid at the specified bounds check instruction in a loop,
// and may be used to hoist ins.
static inline bool SymbolicBoundIsValid(MBasicBlock* header, MBoundsCheck* ins,
                                        const SymbolicBound* bound) {
  if (!bound->loop) return true;
  if (ins->block() == header) return false;
  MBasicBlock* bb = ins->block()->immediateDominator();
  while (bb != header && bb != bound->loop->test->block())
    bb = bb->immediateDominator();
  return bb == bound->loop->test->block();
}

bool RangeAnalysis::tryHoistBoundsCheck(MBasicBlock* header,
                                        MBoundsCheck* ins) {
  // The bounds check's length must be loop invariant.
  MDefinition* length = DefinitionOrBetaInputDefinition(ins->length());
  if (length->block()->isMarked()) return false;

  // The bounds check's index should not be loop invariant (else we would
  // already have hoisted it during LICM).
  SimpleLinearSum index = ExtractLinearSum(ins->index());
  if (!index.term || !index.term->block()->isMarked()) return false;

  // Check for a symbolic lower and upper bound on the index. If either
  // condition depends on an iteration bound for the loop, only hoist if
  // the bounds check is dominated by the iteration bound's test.
  if (!index.term->range()) return false;
  const SymbolicBound* lower = index.term->range()->symbolicLower();
  if (!lower || !SymbolicBoundIsValid(header, ins, lower)) return false;
  const SymbolicBound* upper = index.term->range()->symbolicUpper();
  if (!upper || !SymbolicBoundIsValid(header, ins, upper)) return false;

  MBasicBlock* preLoop = header->loopPredecessor();
  MOZ_ASSERT(!preLoop->isMarked());

  MDefinition* lowerTerm = ConvertLinearSum(alloc(), preLoop, lower->sum);
  if (!lowerTerm) return false;

  MDefinition* upperTerm = ConvertLinearSum(alloc(), preLoop, upper->sum);
  if (!upperTerm) return false;

  // We are checking that index + indexConstant >= 0, and know that
  // index >= lowerTerm + lowerConstant. Thus, check that:
  //
  // lowerTerm + lowerConstant + indexConstant >= 0
  // lowerTerm >= -lowerConstant - indexConstant

  int32_t lowerConstant = 0;
  if (!SafeSub(lowerConstant, index.constant, &lowerConstant)) return false;
  if (!SafeSub(lowerConstant, lower->sum.constant(), &lowerConstant))
    return false;

  // We are checking that index < boundsLength, and know that
  // index <= upperTerm + upperConstant. Thus, check that:
  //
  // upperTerm + upperConstant < boundsLength

  int32_t upperConstant = index.constant;
  if (!SafeAdd(upper->sum.constant(), upperConstant, &upperConstant))
    return false;

  // Hoist the loop invariant lower bounds checks.
  MBoundsCheckLower* lowerCheck = MBoundsCheckLower::New(alloc(), lowerTerm);
  lowerCheck->setMinimum(lowerConstant);
  lowerCheck->computeRange(alloc());
  lowerCheck->collectRangeInfoPreTrunc();
  preLoop->insertBefore(preLoop->lastIns(), lowerCheck);

  // Hoist the loop invariant upper bounds checks.
  if (upperTerm != length || upperConstant >= 0) {
    MBoundsCheck* upperCheck = MBoundsCheck::New(alloc(), upperTerm, length);
    upperCheck->setMinimum(upperConstant);
    upperCheck->setMaximum(upperConstant);
    upperCheck->computeRange(alloc());
    upperCheck->collectRangeInfoPreTrunc();
    preLoop->insertBefore(preLoop->lastIns(), upperCheck);
  }

  return true;
}

bool RangeAnalysis::analyze() {
  JitSpew(JitSpew_Range, "Doing range propagation");

  for (ReversePostorderIterator iter(graph_.rpoBegin());
       iter != graph_.rpoEnd(); iter++) {
    MBasicBlock* block = *iter;
    // No blocks are supposed to be unreachable, except when we have an OSR
    // block, in which case the Value Numbering phase add fixup blocks which
    // are unreachable.
    MOZ_ASSERT(!block->unreachable() || graph_.osrBlock());

    // If the block's immediate dominator is unreachable, the block is
    // unreachable. Iterating in RPO, we'll always see the immediate
    // dominator before the block.
    if (block->immediateDominator()->unreachable()) {
      block->setUnreachableUnchecked();
      continue;
    }

    for (MDefinitionIterator iter(block); iter; iter++) {
      MDefinition* def = *iter;
      if (!alloc().ensureBallast()) return false;

      def->computeRange(alloc());
      JitSpew(JitSpew_Range, "computing range on %d", def->id());
      SpewRange(def);
    }

    // Beta node range analysis may have marked this block unreachable. If
    // so, it's no longer interesting to continue processing it.
    if (block->unreachable()) continue;

    if (block->isLoopHeader()) {
      if (!analyzeLoop(block)) return false;
    }

    // First pass at collecting range info - while the beta nodes are still
    // around and before truncation.
    for (MInstructionIterator iter(block->begin()); iter != block->end();
         iter++)
      iter->collectRangeInfoPreTrunc();
  }

  return true;
}

bool RangeAnalysis::addRangeAssertions() {
  if (!JitOptions.checkRangeAnalysis) return true;

  // Check the computed range for this instruction, if the option is set. Note
  // that this code is quite invasive; it adds numerous additional
  // instructions for each MInstruction with a computed range, and it uses
  // registers, so it also affects register allocation.
  for (ReversePostorderIterator iter(graph_.rpoBegin());
       iter != graph_.rpoEnd(); iter++) {
    MBasicBlock* block = *iter;

    // Do not add assertions in unreachable blocks.
    if (block->unreachable()) continue;

    for (MDefinitionIterator iter(block); iter; iter++) {
      MDefinition* ins = *iter;

      // Perform range checking for all numeric and numeric-like types.
      if (!IsNumberType(ins->type()) && ins->type() != MIRType::Boolean &&
          ins->type() != MIRType::Value) {
        continue;
      }

      // MIsNoIter is fused with the MTest that follows it and emitted as
      // LIsNoIterAndBranch. Skip it to avoid complicating MIsNoIter
      // lowering.
      if (ins->isIsNoIter()) continue;

      Range r(ins);

      MOZ_ASSERT_IF(ins->type() == MIRType::Int64, r.isUnknown());

      // Don't insert assertions if there's nothing interesting to assert.
      if (r.isUnknown() ||
          (ins->type() == MIRType::Int32 && r.isUnknownInt32()))
        continue;

      // Don't add a use to an instruction that is recovered on bailout.
      if (ins->isRecoveredOnBailout()) continue;

      if (!alloc().ensureBallast()) return false;
      MAssertRange* guard =
          MAssertRange::New(alloc(), ins, new (alloc()) Range(r));

      // Beta nodes and interrupt checks are required to be located at the
      // beginnings of basic blocks, so we must insert range assertions
      // after any such instructions.
      MInstruction* insertAt = nullptr;
      if (block->graph().osrBlock() == block)
        insertAt = ins->toInstruction();
      else
        insertAt = block->safeInsertTop(ins);

      if (insertAt == *iter)
        block->insertAfter(insertAt, guard);
      else
        block->insertBefore(insertAt, guard);
    }
  }

  return true;
}

///////////////////////////////////////////////////////////////////////////////
// Range based Truncation
///////////////////////////////////////////////////////////////////////////////

void Range::clampToInt32() {
  if (isInt32()) return;
  int32_t l = hasInt32LowerBound() ? lower() : JSVAL_INT_MIN;
  int32_t h = hasInt32UpperBound() ? upper() : JSVAL_INT_MAX;
  setInt32(l, h);
}

void Range::wrapAroundToInt32() {
  if (!hasInt32Bounds()) {
    setInt32(JSVAL_INT_MIN, JSVAL_INT_MAX);
  } else if (canHaveFractionalPart()) {
    // Clearing the fractional field may provide an opportunity to refine
    // lower_ or upper_.
    canHaveFractionalPart_ = ExcludesFractionalParts;
    canBeNegativeZero_ = ExcludesNegativeZero;
    refineInt32BoundsByExponent(max_exponent_, &lower_, &hasInt32LowerBound_,
                                &upper_, &hasInt32UpperBound_);

    assertInvariants();
  } else {
    // If nothing else, we can clear the negative zero flag.
    canBeNegativeZero_ = ExcludesNegativeZero;
  }
  MOZ_ASSERT(isInt32());
}

void Range::wrapAroundToShiftCount() {
  wrapAroundToInt32();
  if (lower() < 0 || upper() >= 32) setInt32(0, 31);
}

void Range::wrapAroundToBoolean() {
  wrapAroundToInt32();
  if (!isBoolean()) setInt32(0, 1);
  MOZ_ASSERT(isBoolean());
}

bool MDefinition::needTruncation(TruncateKind kind) {
  // No procedure defined for truncating this instruction.
  return false;
}

void MDefinition::truncate() {
  MOZ_CRASH("No procedure defined for truncating this instruction.");
}

bool MConstant::needTruncation(TruncateKind kind) {
  return IsFloatingPointType(type());
}

void MConstant::truncate() {
  MOZ_ASSERT(needTruncation(Truncate));

  // Truncate the double to int, since all uses truncates it.
  int32_t res = ToInt32(numberToDouble());
  payload_.asBits = 0;
  payload_.i32 = res;
  setResultType(MIRType::Int32);
  if (range()) range()->setInt32(res, res);
}

bool MPhi::needTruncation(TruncateKind kind) {
  if (type() == MIRType::Double || type() == MIRType::Int32) {
    truncateKind_ = kind;
    return true;
  }

  return false;
}

void MPhi::truncate() {
  setResultType(MIRType::Int32);
  if (truncateKind_ >= IndirectTruncate && range())
    range()->wrapAroundToInt32();
}

bool MAdd::needTruncation(TruncateKind kind) {
  // Remember analysis, needed for fallible checks.
  setTruncateKind(kind);

  return type() == MIRType::Double || type() == MIRType::Int32;
}

void MAdd::truncate() {
  MOZ_ASSERT(needTruncation(truncateKind()));
  specialization_ = MIRType::Int32;
  setResultType(MIRType::Int32);
  if (truncateKind() >= IndirectTruncate && range())
    range()->wrapAroundToInt32();
}

bool MSub::needTruncation(TruncateKind kind) {
  // Remember analysis, needed for fallible checks.
  setTruncateKind(kind);

  return type() == MIRType::Double || type() == MIRType::Int32;
}

void MSub::truncate() {
  MOZ_ASSERT(needTruncation(truncateKind()));
  specialization_ = MIRType::Int32;
  setResultType(MIRType::Int32);
  if (truncateKind() >= IndirectTruncate && range())
    range()->wrapAroundToInt32();
}

bool MMul::needTruncation(TruncateKind kind) {
  // Remember analysis, needed for fallible checks.
  setTruncateKind(kind);

  return type() == MIRType::Double || type() == MIRType::Int32;
}

void MMul::truncate() {
  MOZ_ASSERT(needTruncation(truncateKind()));
  specialization_ = MIRType::Int32;
  setResultType(MIRType::Int32);
  if (truncateKind() >= IndirectTruncate) {
    setCanBeNegativeZero(false);
    if (range()) range()->wrapAroundToInt32();
  }
}

bool MDiv::needTruncation(TruncateKind kind) {
  // Remember analysis, needed for fallible checks.
  setTruncateKind(kind);

  return type() == MIRType::Double || type() == MIRType::Int32;
}

void MDiv::truncate() {
  MOZ_ASSERT(needTruncation(truncateKind()));
  specialization_ = MIRType::Int32;
  setResultType(MIRType::Int32);

  // Divisions where the lhs and rhs are unsigned and the result is
  // truncated can be lowered more efficiently.
  if (unsignedOperands()) {
    replaceWithUnsignedOperands();
    unsigned_ = true;
  }
}

bool MMod::needTruncation(TruncateKind kind) {
  // Remember analysis, needed for fallible checks.
  setTruncateKind(kind);

  return type() == MIRType::Double || type() == MIRType::Int32;
}

void MMod::truncate() {
  // As for division, handle unsigned modulus with a truncated result.
  MOZ_ASSERT(needTruncation(truncateKind()));
  specialization_ = MIRType::Int32;
  setResultType(MIRType::Int32);

  if (unsignedOperands()) {
    replaceWithUnsignedOperands();
    unsigned_ = true;
  }
}

bool MToDouble::needTruncation(TruncateKind kind) {
  MOZ_ASSERT(type() == MIRType::Double);
  setTruncateKind(kind);

  return true;
}

void MToDouble::truncate() {
  MOZ_ASSERT(needTruncation(truncateKind()));

  // We use the return type to flag that this MToDouble should be replaced by
  // a MTruncateToInt32 when modifying the graph.
  setResultType(MIRType::Int32);
  if (truncateKind() >= IndirectTruncate) {
    if (range()) range()->wrapAroundToInt32();
  }
}

bool MLimitedTruncate::needTruncation(TruncateKind kind) {
  setTruncateKind(kind);
  setResultType(MIRType::Int32);
  if (kind >= IndirectTruncate && range()) range()->wrapAroundToInt32();
  return false;
}

bool MCompare::needTruncation(TruncateKind kind) {
  // If we're compiling wasm, don't try to optimize the comparison type, as
  // the code presumably is already using the type it wants. Also, wasm
  // doesn't support bailouts, so we woudn't be able to rely on
  // TruncateAfterBailouts to convert our inputs.
  if (block()->info().compilingWasm()) return false;

  if (!isDoubleComparison()) return false;

  // If both operands are naturally in the int32 range, we can convert from
  // a double comparison to being an int32 comparison.
  if (!Range(lhs()).isInt32() || !Range(rhs()).isInt32()) return false;

  return true;
}

void MCompare::truncate() {
  compareType_ = Compare_Int32;

  // Truncating the operands won't change their value because we don't force a
  // truncation, but it will change their type, which we need because we
  // now expect integer inputs.
  truncateOperands_ = true;
}

MDefinition::TruncateKind MDefinition::operandTruncateKind(size_t index) const {
  // Generic routine: We don't know anything.
  return NoTruncate;
}

MDefinition::TruncateKind MPhi::operandTruncateKind(size_t index) const {
  // The truncation applied to a phi is effectively applied to the phi's
  // operands.
  return truncateKind_;
}

MDefinition::TruncateKind MTruncateToInt32::operandTruncateKind(
    size_t index) const {
  // This operator is an explicit truncate to int32.
  return Truncate;
}

MDefinition::TruncateKind MBinaryBitwiseInstruction::operandTruncateKind(
    size_t index) const {
  // The bitwise operators truncate to int32.
  return Truncate;
}

MDefinition::TruncateKind MLimitedTruncate::operandTruncateKind(
    size_t index) const {
  return Min(truncateKind(), truncateLimit_);
}

MDefinition::TruncateKind MAdd::operandTruncateKind(size_t index) const {
  // This operator is doing some arithmetic. If its result is truncated,
  // it's an indirect truncate for its operands.
  return Min(truncateKind(), IndirectTruncate);
}

MDefinition::TruncateKind MSub::operandTruncateKind(size_t index) const {
  // See the comment in MAdd::operandTruncateKind.
  return Min(truncateKind(), IndirectTruncate);
}

MDefinition::TruncateKind MMul::operandTruncateKind(size_t index) const {
  // See the comment in MAdd::operandTruncateKind.
  return Min(truncateKind(), IndirectTruncate);
}

MDefinition::TruncateKind MToDouble::operandTruncateKind(size_t index) const {
  // MToDouble propagates its truncate kind to its operand.
  return truncateKind();
}

MDefinition::TruncateKind MStoreUnboxedScalar::operandTruncateKind(
    size_t index) const {
  // Some receiver objects, such as typed arrays, will truncate out of range
  // integer inputs.
  return (truncateInput() && index == 2 && isIntegerWrite()) ? Truncate
                                                             : NoTruncate;
}

MDefinition::TruncateKind MStoreTypedArrayElementHole::operandTruncateKind(
    size_t index) const {
  // An integer store truncates the stored value.
  return index == 3 && isIntegerWrite() ? Truncate : NoTruncate;
}

MDefinition::TruncateKind MDiv::operandTruncateKind(size_t index) const {
  return Min(truncateKind(), TruncateAfterBailouts);
}

MDefinition::TruncateKind MMod::operandTruncateKind(size_t index) const {
  return Min(truncateKind(), TruncateAfterBailouts);
}

MDefinition::TruncateKind MCompare::operandTruncateKind(size_t index) const {
  // If we're doing an int32 comparison on operands which were previously
  // floating-point, convert them!
  MOZ_ASSERT_IF(truncateOperands_, isInt32Comparison());
  return truncateOperands_ ? TruncateAfterBailouts : NoTruncate;
}

static bool TruncateTest(TempAllocator& alloc, MTest* test) {
  // If all possible inputs to the test are either int32 or boolean,
  // convert those inputs to int32 so that an int32 test can be performed.

  if (test->input()->type() != MIRType::Value) return true;

  if (!test->input()->isPhi() || !test->input()->hasOneDefUse() ||
      test->input()->isImplicitlyUsed())
    return true;

  MPhi* phi = test->input()->toPhi();
  for (size_t i = 0; i < phi->numOperands(); i++) {
    MDefinition* def = phi->getOperand(i);
    if (!def->isBox()) return true;
    MDefinition* inner = def->getOperand(0);
    if (inner->type() != MIRType::Boolean && inner->type() != MIRType::Int32)
      return true;
  }

  for (size_t i = 0; i < phi->numOperands(); i++) {
    MDefinition* inner = phi->getOperand(i)->getOperand(0);
    if (inner->type() != MIRType::Int32) {
      if (!alloc.ensureBallast()) return false;
      MBasicBlock* block = inner->block();
      inner = MToNumberInt32::New(alloc, inner);
      block->insertBefore(block->lastIns(), inner->toInstruction());
    }
    MOZ_ASSERT(inner->type() == MIRType::Int32);
    phi->replaceOperand(i, inner);
  }

  phi->setResultType(MIRType::Int32);
  return true;
}

// Truncating instruction result is an optimization which implies
// knowing all uses of an instruction.  This implies that if one of
// the uses got removed, then Range Analysis is not be allowed to do
// any modification which can change the result, especially if the
// result can be observed.
//
// This corner can easily be understood with UCE examples, but it
// might also happen with type inference assumptions.  Note: Type
// inference is implicitly branches where other types might be
// flowing into.
static bool CloneForDeadBranches(TempAllocator& alloc,
                                 MInstruction* candidate) {
  // Compare returns a boolean so it doesn't have to be recovered on bailout
  // because the output would remain correct.
  if (candidate->isCompare()) return true;

  MOZ_ASSERT(candidate->canClone());
  if (!alloc.ensureBallast()) return false;

  MDefinitionVector operands(alloc);
  size_t end = candidate->numOperands();
  if (!operands.reserve(end)) return false;
  for (size_t i = 0; i < end; ++i)
    operands.infallibleAppend(candidate->getOperand(i));

  MInstruction* clone = candidate->clone(alloc, operands);
  clone->setRange(nullptr);

  // Set UseRemoved flag on the cloned instruction in order to chain recover
  // instruction for the bailout path.
  clone->setUseRemovedUnchecked();

  candidate->block()->insertBefore(candidate, clone);

  if (!candidate->maybeConstantValue()) {
    MOZ_ASSERT(clone->canRecoverOnBailout());
    clone->setRecoveredOnBailout();
  }

  // Replace the candidate by its recovered on bailout clone within recovered
  // instructions and resume points operands.
  for (MUseIterator i(candidate->usesBegin()); i != candidate->usesEnd();) {
    MUse* use = *i++;
    MNode* ins = use->consumer();
    if (ins->isDefinition() && !ins->toDefinition()->isRecoveredOnBailout())
      continue;

    use->replaceProducer(clone);
  }

  return true;
}

// Examine all the users of |candidate| and determine the most aggressive
// truncate kind that satisfies all of them.
static MDefinition::TruncateKind ComputeRequestedTruncateKind(
    MDefinition* candidate, bool* shouldClone) {
  bool isCapturedResult =
      false;  // Check if used by a recovered instruction or a resume point.
  bool isObservableResult =
      false;  // Check if it can be read from another frame.
  bool isRecoverableResult = true;  // Check if it can safely be reconstructed.
  bool hasUseRemoved = candidate->isUseRemoved();

  MDefinition::TruncateKind kind = MDefinition::Truncate;
  for (MUseIterator use(candidate->usesBegin()); use != candidate->usesEnd();
       use++) {
    if (use->consumer()->isResumePoint()) {
      // Truncation is a destructive optimization, as such, we need to pay
      // attention to removed branches and prevent optimization
      // destructive optimizations if we have no alternative. (see
      // UseRemoved flag)
      isCapturedResult = true;
      isObservableResult =
          isObservableResult ||
          use->consumer()->toResumePoint()->isObservableOperand(*use);
      isRecoverableResult =
          isRecoverableResult &&
          use->consumer()->toResumePoint()->isRecoverableOperand(*use);
      continue;
    }

    MDefinition* consumer = use->consumer()->toDefinition();
    if (consumer->isRecoveredOnBailout()) {
      isCapturedResult = true;
      hasUseRemoved = hasUseRemoved || consumer->isUseRemoved();
      continue;
    }

    MDefinition::TruncateKind consumerKind =
        consumer->operandTruncateKind(consumer->indexOf(*use));
    kind = Min(kind, consumerKind);
    if (kind == MDefinition::NoTruncate) break;
  }

  // We cannot do full trunction on guarded instructions.
  if (candidate->isGuard() || candidate->isGuardRangeBailouts())
    kind = Min(kind, MDefinition::TruncateAfterBailouts);

  // If the value naturally produces an int32 value (before bailout checks)
  // that needs no conversion, we don't have to worry about resume points
  // seeing truncated values.
  bool needsConversion = !candidate->range() || !candidate->range()->isInt32();

  // If the instruction is explicitly truncated (not indirectly) by all its
  // uses and if it has no removed uses, then we can safely encode its
  // truncated result as part of the resume point operands.  This is safe,
  // because even if we resume with a truncated double, the next baseline
  // instruction operating on this instruction is going to be a no-op.
  //
  // Note, that if the result can be observed from another frame, then this
  // optimization is not safe.
  bool safeToConvert =
      kind == MDefinition::Truncate && !hasUseRemoved && !isObservableResult;

  // If the candidate instruction appears as operand of a resume point or a
  // recover instruction, and we have to truncate its result, then we might
  // have to either recover the result during the bailout, or avoid the
  // truncation.
  if (isCapturedResult && needsConversion && !safeToConvert) {
    // If the result can be recovered from all the resume points (not needed
    // for iterating over the inlined frames), and this instruction can be
    // recovered on bailout, then we can clone it and use the cloned
    // instruction to encode the recover instruction.  Otherwise, we should
    // keep the original result and bailout if the value is not in the int32
    // range.
    if (!JitOptions.disableRecoverIns && isRecoverableResult &&
        candidate->canRecoverOnBailout())
      *shouldClone = true;
    else
      kind = Min(kind, MDefinition::TruncateAfterBailouts);
  }

  return kind;
}

static MDefinition::TruncateKind ComputeTruncateKind(MDefinition* candidate,
                                                     bool* shouldClone) {
  // Compare operations might coerce its inputs to int32 if the ranges are
  // correct.  So we do not need to check if all uses are coerced.
  if (candidate->isCompare()) return MDefinition::TruncateAfterBailouts;

  // Set truncated flag if range analysis ensure that it has no
  // rounding errors and no fractional part. Note that we can't use
  // the MDefinition Range constructor, because we need to know if
  // the value will have rounding errors before any bailout checks.
  const Range* r = candidate->range();
  bool canHaveRoundingErrors = !r || r->canHaveRoundingErrors();

  // Special case integer division and modulo: a/b can be infinite, and a%b
  // can be NaN but cannot actually have rounding errors induced by truncation.
  if ((candidate->isDiv() || candidate->isMod()) &&
      static_cast<const MBinaryArithInstruction*>(candidate)
              ->specialization() == MIRType::Int32) {
    canHaveRoundingErrors = false;
  }

  if (canHaveRoundingErrors) return MDefinition::NoTruncate;

  // Ensure all observable uses are truncated.
  return ComputeRequestedTruncateKind(candidate, shouldClone);
}

static void RemoveTruncatesOnOutput(MDefinition* truncated) {
  // Compare returns a boolean so it doen't have any output truncates.
  if (truncated->isCompare()) return;

  MOZ_ASSERT(truncated->type() == MIRType::Int32);
  MOZ_ASSERT(Range(truncated).isInt32());

  for (MUseDefIterator use(truncated); use; use++) {
    MDefinition* def = use.def();
    if (!def->isTruncateToInt32() || !def->isToNumberInt32()) continue;

    def->replaceAllUsesWith(truncated);
  }
}

static void AdjustTruncatedInputs(TempAllocator& alloc,
                                  MDefinition* truncated) {
  MBasicBlock* block = truncated->block();
  for (size_t i = 0, e = truncated->numOperands(); i < e; i++) {
    MDefinition::TruncateKind kind = truncated->operandTruncateKind(i);
    if (kind == MDefinition::NoTruncate) continue;

    MDefinition* input = truncated->getOperand(i);
    if (input->type() == MIRType::Int32) continue;

    if (input->isToDouble() && input->getOperand(0)->type() == MIRType::Int32) {
      truncated->replaceOperand(i, input->getOperand(0));
    } else {
      MInstruction* op;
      if (kind == MDefinition::TruncateAfterBailouts)
        op = MToNumberInt32::New(alloc, truncated->getOperand(i));
      else
        op = MTruncateToInt32::New(alloc, truncated->getOperand(i));

      if (truncated->isPhi()) {
        MBasicBlock* pred = block->getPredecessor(i);
        pred->insertBefore(pred->lastIns(), op);
      } else {
        block->insertBefore(truncated->toInstruction(), op);
      }
      truncated->replaceOperand(i, op);
    }
  }

  if (truncated->isToDouble()) {
    truncated->replaceAllUsesWith(truncated->toToDouble()->getOperand(0));
    block->discard(truncated->toToDouble());
  }
}

// Iterate backward on all instruction and attempt to truncate operations for
// each instruction which respect the following list of predicates: Has been
// analyzed by range analysis, the range has no rounding errors, all uses cases
// are truncating the result.
//
// If the truncation of the operation is successful, then the instruction is
// queue for later updating the graph to restore the type correctness by
// converting the operands that need to be truncated.
//
// We iterate backward because it is likely that a truncated operation truncates
// some of its operands.
bool RangeAnalysis::truncate() {
  JitSpew(JitSpew_Range, "Do range-base truncation (backward loop)");

  // Automatic truncation is disabled for wasm because the truncation logic
  // is based on IonMonkey which assumes that we can bailout if the truncation
  // logic fails. As wasm code has no bailout mechanism, it is safer to avoid
  // any automatic truncations.
  MOZ_ASSERT(!mir->compilingWasm());

  Vector<MDefinition*, 16, SystemAllocPolicy> worklist;

  for (PostorderIterator block(graph_.poBegin()); block != graph_.poEnd();
       block++) {
    for (MInstructionReverseIterator iter(block->rbegin());
         iter != block->rend(); iter++) {
      if (iter->isRecoveredOnBailout()) continue;

      if (iter->type() == MIRType::None) {
        if (iter->isTest()) {
          if (!TruncateTest(alloc(), iter->toTest())) return false;
        }
        continue;
      }

      // Remember all bitop instructions for folding after range analysis.
      switch (iter->op()) {
        case MDefinition::Opcode::BitAnd:
        case MDefinition::Opcode::BitOr:
        case MDefinition::Opcode::BitXor:
        case MDefinition::Opcode::Lsh:
        case MDefinition::Opcode::Rsh:
        case MDefinition::Opcode::Ursh:
          if (!bitops.append(static_cast<MBinaryBitwiseInstruction*>(*iter)))
            return false;
          break;
        default:;
      }

      bool shouldClone = false;
      MDefinition::TruncateKind kind = ComputeTruncateKind(*iter, &shouldClone);
      if (kind == MDefinition::NoTruncate) continue;

      // Range Analysis is sometimes eager to do optimizations, even if we
      // are not be able to truncate an instruction. In such case, we
      // speculatively compile the instruction to an int32 instruction
      // while adding a guard. This is what is implied by
      // TruncateAfterBailout.
      //
      // If we already experienced an overflow bailout while executing
      // code within the current JSScript, we no longer attempt to make
      // this kind of eager optimizations.
      if (kind <= MDefinition::TruncateAfterBailouts &&
          block->info().hadOverflowBailout())
        continue;

      // Truncate this instruction if possible.
      if (!iter->needTruncation(kind)) continue;

      SpewTruncate(*iter, kind, shouldClone);

      // If needed, clone the current instruction for keeping it for the
      // bailout path.  This give us the ability to truncate instructions
      // even after the removal of branches.
      if (shouldClone && !CloneForDeadBranches(alloc(), *iter)) return false;

      iter->truncate();

      // Delay updates of inputs/outputs to avoid creating node which
      // would be removed by the truncation of the next operations.
      iter->setInWorklist();
      if (!worklist.append(*iter)) return false;
    }
    for (MPhiIterator iter(block->phisBegin()), end(block->phisEnd());
         iter != end; ++iter) {
      bool shouldClone = false;
      MDefinition::TruncateKind kind = ComputeTruncateKind(*iter, &shouldClone);
      if (kind == MDefinition::NoTruncate) continue;

      // Truncate this phi if possible.
      if (shouldClone || !iter->needTruncation(kind)) continue;

      SpewTruncate(*iter, kind, shouldClone);

      iter->truncate();

      // Delay updates of inputs/outputs to avoid creating node which
      // would be removed by the truncation of the next operations.
      iter->setInWorklist();
      if (!worklist.append(*iter)) return false;
    }
  }

  // Update inputs/outputs of truncated instructions.
  JitSpew(JitSpew_Range, "Do graph type fixup (dequeue)");
  while (!worklist.empty()) {
    if (!alloc().ensureBallast()) return false;
    MDefinition* def = worklist.popCopy();
    def->setNotInWorklist();
    RemoveTruncatesOnOutput(def);
    AdjustTruncatedInputs(alloc(), def);
  }

  return true;
}

bool RangeAnalysis::removeUnnecessaryBitops() {
  // Note: This operation change the semantic of the program in a way which
  // uniquely works with Int32, Recover Instructions added by the Sink phase
  // expects the MIR Graph to still have a valid flow as-if they were double
  // operations instead of Int32 operations. Thus, this phase should be
  // executed after the Sink phase, and before DCE.

  // Fold any unnecessary bitops in the graph, such as (x | 0) on an integer
  // input. This is done after range analysis rather than during GVN as the
  // presence of the bitop can change which instructions are truncated.
  for (size_t i = 0; i < bitops.length(); i++) {
    MBinaryBitwiseInstruction* ins = bitops[i];
    if (ins->isRecoveredOnBailout()) continue;

    MDefinition* folded = ins->foldUnnecessaryBitop();
    if (folded != ins) {
      ins->replaceAllLiveUsesWith(folded);
      ins->setRecoveredOnBailout();
    }
  }

  bitops.clear();
  return true;
}

///////////////////////////////////////////////////////////////////////////////
// Collect Range information of operands
///////////////////////////////////////////////////////////////////////////////

void MInArray::collectRangeInfoPreTrunc() {
  Range indexRange(index());
  if (indexRange.isFiniteNonNegative()) needsNegativeIntCheck_ = false;
}

void MLoadElementHole::collectRangeInfoPreTrunc() {
  Range indexRange(index());
  if (indexRange.isFiniteNonNegative()) {
    needsNegativeIntCheck_ = false;
    setNotGuard();
  }
}

void MClz::collectRangeInfoPreTrunc() {
  Range inputRange(input());
  if (!inputRange.canBeZero()) operandIsNeverZero_ = true;
}

void MCtz::collectRangeInfoPreTrunc() {
  Range inputRange(input());
  if (!inputRange.canBeZero()) operandIsNeverZero_ = true;
}

void MDiv::collectRangeInfoPreTrunc() {
  Range lhsRange(lhs());
  Range rhsRange(rhs());

  // Test if Dividend is non-negative.
  if (lhsRange.isFiniteNonNegative()) canBeNegativeDividend_ = false;

  // Try removing divide by zero check.
  if (!rhsRange.canBeZero()) canBeDivideByZero_ = false;

  // If lhsRange does not contain INT32_MIN in its range,
  // negative overflow check can be skipped.
  if (!lhsRange.contains(INT32_MIN)) canBeNegativeOverflow_ = false;

  // If rhsRange does not contain -1 likewise.
  if (!rhsRange.contains(-1)) canBeNegativeOverflow_ = false;

  // If lhsRange does not contain a zero,
  // negative zero check can be skipped.
  if (!lhsRange.canBeZero()) canBeNegativeZero_ = false;

  // If rhsRange >= 0 negative zero check can be skipped.
  if (rhsRange.isFiniteNonNegative()) canBeNegativeZero_ = false;
}

void MMul::collectRangeInfoPreTrunc() {
  Range lhsRange(lhs());
  Range rhsRange(rhs());

  // If lhsRange contains only positive then we can skip negative zero check.
  if (lhsRange.isFiniteNonNegative() && !lhsRange.canBeZero())
    setCanBeNegativeZero(false);

  // Likewise rhsRange.
  if (rhsRange.isFiniteNonNegative() && !rhsRange.canBeZero())
    setCanBeNegativeZero(false);

  // If rhsRange and lhsRange contain Non-negative integers only,
  // We skip negative zero check.
  if (rhsRange.isFiniteNonNegative() && lhsRange.isFiniteNonNegative())
    setCanBeNegativeZero(false);

  // If rhsRange and lhsRange < 0. Then we skip negative zero check.
  if (rhsRange.isFiniteNegative() && lhsRange.isFiniteNegative())
    setCanBeNegativeZero(false);
}

void MMod::collectRangeInfoPreTrunc() {
  Range lhsRange(lhs());
  Range rhsRange(rhs());
  if (lhsRange.isFiniteNonNegative()) canBeNegativeDividend_ = false;
  if (!rhsRange.canBeZero()) canBeDivideByZero_ = false;
}

void MToNumberInt32::collectRangeInfoPreTrunc() {
  Range inputRange(input());
  if (!inputRange.canBeNegativeZero()) canBeNegativeZero_ = false;
}

void MBoundsCheck::collectRangeInfoPreTrunc() {
  Range indexRange(index());
  Range lengthRange(length());
  if (!indexRange.hasInt32LowerBound() || !indexRange.hasInt32UpperBound())
    return;
  if (!lengthRange.hasInt32LowerBound() || lengthRange.canBeNaN()) return;

  int64_t indexLower = indexRange.lower();
  int64_t indexUpper = indexRange.upper();
  int64_t lengthLower = lengthRange.lower();
  int64_t min = minimum();
  int64_t max = maximum();

  if (indexLower + min >= 0 && indexUpper + max < lengthLower)
    fallible_ = false;
}

void MBoundsCheckLower::collectRangeInfoPreTrunc() {
  Range indexRange(index());
  if (indexRange.hasInt32LowerBound() && indexRange.lower() >= minimum_)
    fallible_ = false;
}

void MCompare::collectRangeInfoPreTrunc() {
  if (!Range(lhs()).canBeNaN() && !Range(rhs()).canBeNaN())
    operandsAreNeverNaN_ = true;
}

void MNot::collectRangeInfoPreTrunc() {
  if (!Range(input()).canBeNaN()) operandIsNeverNaN_ = true;
}

void MPowHalf::collectRangeInfoPreTrunc() {
  Range inputRange(input());
  if (!inputRange.canBeInfiniteOrNaN() || inputRange.hasInt32LowerBound())
    operandIsNeverNegativeInfinity_ = true;
  if (!inputRange.canBeNegativeZero()) operandIsNeverNegativeZero_ = true;
  if (!inputRange.canBeNaN()) operandIsNeverNaN_ = true;
}

void MUrsh::collectRangeInfoPreTrunc() {
  if (specialization_ == MIRType::Int64) return;

  Range lhsRange(lhs()), rhsRange(rhs());

  // As in MUrsh::computeRange(), convert the inputs.
  lhsRange.wrapAroundToInt32();
  rhsRange.wrapAroundToShiftCount();

  // If the most significant bit of our result is always going to be zero,
  // we can optimize by disabling bailout checks for enforcing an int32 range.
  if (lhsRange.lower() >= 0 || rhsRange.lower() >= 1) bailoutsDisabled_ = true;
}

static bool DoesMaskMatchRange(int32_t mask, Range& range) {
  // Check if range is positive, because the bitand operator in `(-3) & 0xff`
  // can't be eliminated.
  if (range.lower() >= 0) {
    MOZ_ASSERT(range.isInt32());
    // Check that the mask value has all bits set given the range upper bound.
    // Note that the upper bound does not have to be exactly the mask value. For
    // example, consider `x & 0xfff` where `x` is a uint8. That expression can
    // still be optimized to `x`.
    int bits = 1 + FloorLog2(range.upper());
    uint32_t maskNeeded = (bits == 32) ? 0xffffffff : (uint32_t(1) << bits) - 1;
    if ((mask & maskNeeded) == maskNeeded) return true;
  }

  return false;
}

void MBinaryBitwiseInstruction::collectRangeInfoPreTrunc() {
  Range lhsRange(lhs());
  Range rhsRange(rhs());

  if (lhs()->isConstant() && lhs()->type() == MIRType::Int32 &&
      DoesMaskMatchRange(lhs()->toConstant()->toInt32(), rhsRange)) {
    maskMatchesRightRange = true;
  }

  if (rhs()->isConstant() && rhs()->type() == MIRType::Int32 &&
      DoesMaskMatchRange(rhs()->toConstant()->toInt32(), lhsRange)) {
    maskMatchesLeftRange = true;
  }
}

void MNaNToZero::collectRangeInfoPreTrunc() {
  Range inputRange(input());

  if (!inputRange.canBeNaN()) operandIsNeverNaN_ = true;
  if (!inputRange.canBeNegativeZero()) operandIsNeverNegativeZero_ = true;
}

bool RangeAnalysis::prepareForUCE(bool* shouldRemoveDeadCode) {
  *shouldRemoveDeadCode = false;

  for (ReversePostorderIterator iter(graph_.rpoBegin());
       iter != graph_.rpoEnd(); iter++) {
    MBasicBlock* block = *iter;

    if (!block->unreachable()) continue;

    // Filter out unreachable fake entries.
    if (block->numPredecessors() == 0) {
      // Ignore fixup blocks added by the Value Numbering phase, in order
      // to keep the dominator tree as-is when we have OSR Block which are
      // no longer reachable from the main entry point of the graph.
      MOZ_ASSERT(graph_.osrBlock());
      continue;
    }

    MControlInstruction* cond = block->getPredecessor(0)->lastIns();
    if (!cond->isTest()) continue;

    // Replace the condition of the test control instruction by a constant
    // chosen based which of the successors has the unreachable flag which is
    // added by MBeta::computeRange on its own block.
    MTest* test = cond->toTest();
    MDefinition* condition = test->input();

    // If the false-branch is unreachable, then the test condition must be true.
    // If the true-branch is unreachable, then the test condition must be false.
    MOZ_ASSERT(block == test->ifTrue() || block == test->ifFalse());
    bool value = block == test->ifFalse();
    MConstant* constant =
        MConstant::New(alloc().fallible(), BooleanValue(value));
    if (!constant) return false;

    condition->setGuardRangeBailoutsUnchecked();

    test->block()->insertBefore(test, constant);

    test->replaceOperand(0, constant);
    JitSpew(JitSpew_Range,
            "Update condition of %d to reflect unreachable branches.",
            test->id());

    *shouldRemoveDeadCode = true;
  }

  return tryRemovingGuards();
}

bool RangeAnalysis::tryRemovingGuards() {
  MDefinitionVector guards(alloc());

  for (ReversePostorderIterator block = graph_.rpoBegin();
       block != graph_.rpoEnd(); block++) {
    for (MDefinitionIterator iter(*block); iter; iter++) {
      if (!iter->isGuardRangeBailouts()) continue;

      iter->setInWorklist();
      if (!guards.append(*iter)) return false;
    }
  }

  // Flag all fallible instructions which were indirectly used in the
  // computation of the condition, such that we do not ignore
  // bailout-paths which are used to shrink the input range of the
  // operands of the condition.
  for (size_t i = 0; i < guards.length(); i++) {
    MDefinition* guard = guards[i];

    // If this ins is a guard even without guardRangeBailouts,
    // there is no reason in trying to hoist the guardRangeBailouts check.
    guard->setNotGuardRangeBailouts();
    if (!DeadIfUnused(guard)) {
      guard->setGuardRangeBailouts();
      continue;
    }
    guard->setGuardRangeBailouts();

    if (!guard->isPhi()) {
      if (!guard->range()) continue;

      // Filter the range of the instruction based on its MIRType.
      Range typeFilteredRange(guard);

      // If the output range is updated by adding the inner range,
      // then the MIRType act as an effectful filter. As we do not know if
      // this filtered Range might change or not the result of the
      // previous comparison, we have to keep this instruction as a guard
      // because it has to bailout in order to restrict the Range to its
      // MIRType.
      if (typeFilteredRange.update(guard->range())) continue;
    }

    guard->setNotGuardRangeBailouts();

    // Propagate the guard to its operands.
    for (size_t op = 0, e = guard->numOperands(); op < e; op++) {
      MDefinition* operand = guard->getOperand(op);

      // Already marked.
      if (operand->isInWorklist()) continue;

      MOZ_ASSERT(!operand->isGuardRangeBailouts());

      operand->setInWorklist();
      operand->setGuardRangeBailouts();
      if (!guards.append(operand)) return false;
    }
  }

  for (size_t i = 0; i < guards.length(); i++) {
    MDefinition* guard = guards[i];
    guard->setNotInWorklist();
  }

  return true;
}