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 /* -*- 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 "jsanalyze.h"

 #include "jit/Ion.h"

 #include "jit/IonAnalysis.h"

 #include "jit/IonSpewer.h"

 #include "jit/MIR.h"

 #include "jit/MIRGenerator.h"

 #include "jit/MIRGraph.h"

 #include "vm/NumericConversions.h"

 #include "jsopcodeinlines.h"

 using namespace js;

 using namespace js::jit;

 using mozilla::Abs;

 using mozilla::CountLeadingZeroes32;

 using mozilla::NumberEqualsInt32;

 using mozilla::ExponentComponent;

 using mozilla::FloorLog2;

 using mozilla::IsInfinite;

 using mozilla::IsNaN;

 using mozilla::IsNegative;

 using mozilla::NegativeInfinity;

 using mozilla::PositiveInfinity;

 using mozilla::Swap;

 using JS::GenericNaN;

 // 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)

         return block->dominates(n->block()->getPredecessor(use->index()));

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

 }

 static inline void

 SpewRange(MDefinition *def)

 {

 #ifdef DEBUG

     if (IonSpewEnabled(IonSpew_Range) && def->type() != MIRType_None && def->range()) {

         IonSpewHeader(IonSpew_Range);

         def->printName(IonSpewFile);

         fprintf(IonSpewFile, " has range ");

         def->range()->dump(IonSpewFile);

     }

 #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(); ) {

         if (i->consumer() != dom && IsDominatedUse(block, *i))

             i = i->consumer()->replaceOperand(i, dom);

         else

             i++;

     }

 }

 bool

 RangeAnalysis::addBetaNodes()

 {

     IonSpew(IonSpew_Range, "Adding beta nodes");

     for (PostorderIterator i(graph_.poBegin()); i != graph_.poEnd(); i++) {

         MBasicBlock *block = *i;

         IonSpew(IonSpew_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();

         // 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();

         }

         if (left->isConstant() && left->toConstant()->value().isNumber()) {

             bound = left->toConstant()->value().toNumber();

             val = right;

             jsop = ReverseCompareOp(jsop);

         } else if (right->isConstant() && right->toConstant()->value().isNumber()) {

             bound = right->toConstant()->value().toNumber();

             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) {

                 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);

                 IonSpew(IonSpew_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);

                 IonSpew(IonSpew_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.

         JS_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);

             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);

             break;

           case JSOP_EQ:

             comp.setDouble(bound, bound);

             break;

           default:

             continue; // well, for neq we could have

                       // [-\inf, bound-1] U [bound+1, \inf] but we only use contiguous ranges.

         }

         if (IonSpewEnabled(IonSpew_Range)) {

             IonSpewHeader(IonSpew_Range);

             fprintf(IonSpewFile, "Adding beta node for %d with range ", val->id());

             comp.dump(IonSpewFile);

         }

         MBeta *beta = MBeta::New(alloc(), val, new(alloc()) Range(comp));

         block->insertBefore(*block->begin(), beta);

         replaceDominatedUsesWith(val, beta, block);

     }

     return true;

 }

 bool

 RangeAnalysis::removeBetaNodes()

 {

     IonSpew(IonSpew_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);

                 IonSpew(IonSpew_Range, "Removing beta node %d for %d",

                         def->id(), op->id());

                 def->replaceAllUsesWith(op);

                 iter = block->discardDefAt(iter);

             } 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::print(Sprinter &sp) const

 {

     if (loop)

         sp.printf("[loop] ");

     sum.print(sp);

 }

 void

 SymbolicBound::dump() const

 {

     Sprinter sp(GetIonContext()->cx);

     sp.init();

     print(sp);

     fprintf(stderr, "%s\n", sp.string());

 }

 // 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::print(Sprinter &sp) const

 {

     assertInvariants();

     // Floating-point or Integer subset.

     if (canHaveFractionalPart_)

         sp.printf("F");

     else

         sp.printf("I");

     sp.printf("[");

     if (!hasInt32LowerBound_)

         sp.printf("?");

     else

         sp.printf("%d", lower_);

     if (symbolicLower_) {

         sp.printf(" {");

         symbolicLower_->print(sp);

         sp.printf("}");

     }

     sp.printf(", ");

     if (!hasInt32UpperBound_)

         sp.printf("?");

     else

         sp.printf("%d", upper_);

     if (symbolicUpper_) {

         sp.printf(" {");

         symbolicUpper_->print(sp);

         sp.printf("}");

     }

     sp.printf("]");

     if (IsExponentInteresting(this)) {

         if (max_exponent_ == IncludesInfinityAndNaN)

             sp.printf(" (U inf U NaN)", max_exponent_);

         else if (max_exponent_ == IncludesInfinity)

             sp.printf(" (U inf)");

         else

             sp.printf(" (< pow(2, %d+1))", max_exponent_);

     }

 }

 void

 Range::dump(FILE *fp) const

 {

     Sprinter sp(GetIonContext()->cx);

     sp.init();

     print(sp);

     fprintf(fp, "%s\n", sp.string());

 }

 void

 Range::dump() const

 {

     dump(stderr);

 }

 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_);

     // :TODO: This information could be used better. If upper < lower, then we

     // have conflicting constraints. Consider:

     //

     // if (x < 0) {

     //   if (x > 0) {

     //     [Some code.]

     //   }

     // }

     //

     // In this case, the block is dead. Right now, we just disregard this fact

     // and make the range unbounded, rather than empty.

     //

     // Instead, we should use it to eliminate the dead block.

     // (Bug 765127)

     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_;

     bool newFractional = lhs->canHaveFractionalPart_ && rhs->canHaveFractionalPart_;

     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, &newUpper);

         // 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,

                             newFractional, 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_;

     bool newFractional = canHaveFractionalPart_ || other->canHaveFractionalPart_;

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

     rawInitialize(newLower, newHasInt32LowerBound, newUpper, newHasInt32UpperBound,

                   newFractional, 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.

         switch (def->type()) {

           case MIRType_Int32:

             wrapAroundToInt32();

             break;

           case MIRType_Boolean:

             wrapAroundToBoolean();

             break;

           case MIRType_None:

             MOZ_ASSUME_UNREACHABLE("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_ASSUME_UNREACHABLE("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())

         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)

 {

     // Infer lower_, upper_, hasInt32LowerBound_, and hasInt32UpperBound_.

     if (l >= INT32_MIN && l <= INT32_MAX) {

         lower_ = int32_t(floor(l));

         hasInt32LowerBound_ = true;

     } else {

         lower_ = INT32_MIN;

         hasInt32LowerBound_ = false;

     }

     if (h >= INT32_MIN && h <= INT32_MAX) {

         upper_ = int32_t(ceil(h));

         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);

     // Infer the canHaveFractionalPart_ field. 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;

     canHaveFractionalPart_ = crossesZero || minExp < MaxTruncatableExponent;

     optimize();

 }

 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, lhs->canHaveFractionalPart() || rhs->canHaveFractionalPart(), 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, lhs->canHaveFractionalPart() || rhs->canHaveFractionalPart(), e);

 }

 Range *

 Range::and_(TempAllocator &alloc, const Range *lhs, const Range *rhs)

 {

     JS_ASSERT(lhs->isInt32());

     JS_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)

 {

     JS_ASSERT(lhs->isInt32());

     JS_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.

     JS_ASSERT_IF(lhs->lower() >= 0, lhs->upper() != 0);

     JS_ASSERT_IF(rhs->lower() >= 0, rhs->upper() != 0);

     JS_ASSERT_IF(lhs->upper() < 0, lhs->lower() != -1);

     JS_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)

 {

     JS_ASSERT(lhs->isInt32());

     JS_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)

 {

     JS_ASSERT(op->isInt32());

     return Range::NewInt32Range(alloc, ~op->upper(), ~op->lower());

 }

 Range *

 Range::mul(TempAllocator &alloc, const Range *lhs, const Range *rhs)

 {

     bool fractional = lhs->canHaveFractionalPart() || rhs->canHaveFractionalPart();

     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, fractional, 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) ),

         fractional, exponent);

 }

 Range *

 Range::lsh(TempAllocator &alloc, const Range *lhs, int32_t c)

 {

     JS_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)

 {

     JS_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.

     JS_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)

 {

     JS_ASSERT(lhs->isInt32());

     JS_ASSERT(rhs->isInt32());

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

 }

 Range *

 Range::rsh(TempAllocator &alloc, const Range *lhs, const Range *rhs)

 {

     JS_ASSERT(lhs->isInt32());

     JS_ASSERT(rhs->isInt32());

     return Range::NewInt32Range(alloc, Min(lhs->lower(), 0), Max(lhs->upper(), 0));

 }

 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.

     JS_ASSERT(lhs->isInt32());

     JS_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_;

     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,

                             op->canHaveFractionalPart_,

                             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;

     return new(alloc) Range(Min(lhs->lower_, rhs->lower_),

                             lhs->hasInt32LowerBound_ && rhs->hasInt32LowerBound_,

                             Min(lhs->upper_, rhs->upper_),

                             lhs->hasInt32UpperBound_ || rhs->hasInt32UpperBound_,

                             lhs->canHaveFractionalPart_ || rhs->canHaveFractionalPart_,

                             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;

     return new(alloc) Range(Max(lhs->lower_, rhs->lower_),

                             lhs->hasInt32LowerBound_ || rhs->hasInt32LowerBound_,

                             Max(lhs->upper_, rhs->upper_),

                             lhs->hasInt32UpperBound_ && rhs->hasInt32UpperBound_,

                             lhs->canHaveFractionalPart_ || rhs->canHaveFractionalPart_,

                             Max(lhs->max_exponent_, rhs->max_exponent_));

 }

 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->canBeFiniteNegative() && rhs->canBeFiniteNonNegative()) ||

            (rhs->canBeFiniteNegative() && 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_ ||

         max_exponent_ != other->max_exponent_;

     if (changed) {

         lower_ = other->lower_;

         hasInt32LowerBound_ = other->hasInt32LowerBound_;

         upper_ = other->upper_;

         hasInt32UpperBound_ = other->hasInt32UpperBound_;

         canHaveFractionalPart_ = other->canHaveFractionalPart_;

         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()) {

             IonSpew(IonSpew_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) {

         IonSpew(IonSpew_Range, "Marking block for inst %d unreachable", id());

         block()->setUnreachable();

     } else {

         setRange(range);

     }

 }

 void

 MConstant::computeRange(TempAllocator &alloc)

 {

     if (value().isNumber()) {

         double d = value().toNumber();

         setRange(Range::NewDoubleRange(alloc, d, d));

     } else if (value().isBoolean()) {

         bool b = value().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)

 {

     Range left(getOperand(0));

     Range right(getOperand(1));

     left.wrapAroundToInt32();

     right.wrapAroundToInt32();

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

 }

 void

 MBitOr::computeRange(TempAllocator &alloc)

 {

     Range left(getOperand(0));

     Range right(getOperand(1));

     left.wrapAroundToInt32();

     right.wrapAroundToInt32();

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

 }

 void

 MBitXor::computeRange(TempAllocator &alloc)

 {

     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)

 {

     Range left(getOperand(0));

     Range right(getOperand(1));

     left.wrapAroundToInt32();

     MDefinition *rhs = getOperand(1);

     if (!rhs->isConstant()) {

         right.wrapAroundToShiftCount();

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

         return;

     }

     int32_t c = rhs->toConstant()->value().toInt32();

     setRange(Range::lsh(alloc, &left, c));

 }

 void

 MRsh::computeRange(TempAllocator &alloc)

 {

     Range left(getOperand(0));

     Range right(getOperand(1));

     left.wrapAroundToInt32();

     MDefinition *rhs = getOperand(1);

     if (!rhs->isConstant()) {

         right.wrapAroundToShiftCount();

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

         return;

     }

     int32_t c = rhs->toConstant()->value().toInt32();

     setRange(Range::rsh(alloc, &left, c));

 }

 void

 MUrsh::computeRange(TempAllocator &alloc)

 {

     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();

     MDefinition *rhs = getOperand(1);

     if (!rhs->isConstant()) {

         setRange(Range::ursh(alloc, &left, &right));

     } else {

         int32_t c = rhs->toConstant()->value().toInt32();

         setRange(Range::ursh(alloc, &left, c));

     }

     JS_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

 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);

     // 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 && lhs.lower() >= 0 && rhs.lower() > 0 &&

         !lhs.canHaveFractionalPart() && !rhs.canHaveFractionalPart())

     {

         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.

         JS_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;

     setRange(new(alloc) Range(lower, upper, lhs.canHaveFractionalPart() || rhs.canHaveFractionalPart(),

                               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(), true, lhs.exponent()));

     } else if (unsigned_ && rhs.lower() >= 1) {

         // We shouldn't set the unsigned flag if the inputs can have

         // fractional parts.

         JS_ASSERT(!lhs.canHaveFractionalPart() && !rhs.canHaveFractionalPart());

         // 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.

     setRange(new(alloc) Range(0, input.upper(), true, 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

 MToInt32::computeRange(TempAllocator &alloc)

 {

     Range *output = new(alloc) Range(getOperand(0));

     output->clampToInt32();

     setRange(output);

 }

 static Range *GetTypedArrayRange(TempAllocator &alloc, int type)

 {

     switch (type) {

       case ScalarTypeDescr::TYPE_UINT8_CLAMPED:

       case ScalarTypeDescr::TYPE_UINT8:

         return Range::NewUInt32Range(alloc, 0, UINT8_MAX);

       case ScalarTypeDescr::TYPE_UINT16:

         return Range::NewUInt32Range(alloc, 0, UINT16_MAX);

       case ScalarTypeDescr::TYPE_UINT32:

         return Range::NewUInt32Range(alloc, 0, UINT32_MAX);

       case ScalarTypeDescr::TYPE_INT8:

         return Range::NewInt32Range(alloc, INT8_MIN, INT8_MAX);

       case ScalarTypeDescr::TYPE_INT16:

         return Range::NewInt32Range(alloc, INT16_MIN, INT16_MAX);

       case ScalarTypeDescr::TYPE_INT32:

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

       case ScalarTypeDescr::TYPE_FLOAT32:

       case ScalarTypeDescr::TYPE_FLOAT64:

         break;

     }

   return nullptr;

 }

 void

 MLoadTypedArrayElement::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, arrayType()));

 }

 void

 MLoadTypedArrayElementStatic::computeRange(TempAllocator &alloc)

 {

     // We don't currently use MLoadTypedArrayElementStatic for uint32, so we

     // don't have to worry about it returning a value outside our type.

     JS_ASSERT(typedArray_->type() != ScalarTypeDescr::TYPE_UINT32);

     setRange(GetTypedArrayRange(alloc, typedArray_->type()));

 }

 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, JSObject::NELEMENTS_LIMIT));

 }

 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 |TooManyArguments| checks.

     // If exceeded, Ion will not be entered in the first place.

     static_assert(SNAPSHOT_MAX_NARGS <= UINT32_MAX,

                   "NewUInt32Range requires a uint32 value");

     setRange(Range::NewUInt32Range(alloc, 0, SNAPSHOT_MAX_NARGS));

 }

 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

 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:

         if (!opRange.canBeNaN()) {

             // Note that Math.sign(-0) is -0, and we treat -0 as equal to 0.

             int32_t lower = -1;

             int32_t upper = 1;

             if (opRange.hasInt32LowerBound() && opRange.lower() >= 0)

                 lower = 0;

             if (opRange.hasInt32UpperBound() && opRange.upper() <= 0)

                 upper = 0;

             setRange(Range::NewInt32Range(alloc, lower, upper));

         }

         break;

     default:

         break;

     }

 }

 void

 MRandom::computeRange(TempAllocator &alloc)

 {

     setRange(Range::NewDoubleRange(alloc, 0.0, 1.0));

 }

 ///////////////////////////////////////////////////////////////////////////////

 // Range Analysis

 ///////////////////////////////////////////////////////////////////////////////

 bool

 RangeAnalysis::markBlocksInLoopBody(MBasicBlock *header, MBasicBlock *backedge)

 {

     Vector<MBasicBlock *, 16, IonAllocPolicy> worklist(alloc());

     // Mark the header as being in the loop. This terminates the walk.

     header->mark();

     backedge->mark();

     if (!worklist.append(backedge))

         return false;

     // If we haven't reached the loop header yet, walk up the predecessors

     // we haven't seen already.

     while (!worklist.empty()) {

         MBasicBlock *current = worklist.popCopy();

         for (size_t i = 0; i < current->numPredecessors(); i++) {

             MBasicBlock *pred = current->getPredecessor(i);

             if (pred->isMarked())

                 continue;

             pred->mark();

             if (!worklist.append(pred))

                 return false;

         }

     }

     return true;

 }

 bool

 RangeAnalysis::analyzeLoop(MBasicBlock *header)

 {

     JS_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;

     if (!markBlocksInLoopBody(header, backedge))

         return false;

     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()) {

                 iterationBound =

                     analyzeLoopIterationCount(header, branch, direction);

                 if (iterationBound)

                     break;

             }

         }

     } while (block != header);

     if (!iterationBound) {

         graph_.unmarkBlocks();

         return true;

     }

 #ifdef DEBUG

     if (IonSpewEnabled(IonSpew_Range)) {

         Sprinter sp(GetIonContext()->cx);

         sp.init();

         iterationBound->sum.print(sp);

         IonSpew(IonSpew_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(header, iterationBound, *iter);

     if (!mir->compilingAsmJS()) {

         // Try to hoist any bounds checks from the loop using symbolic bounds.

         Vector<MBoundsCheck *, 0, IonAllocPolicy> 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 (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);

         }

     }

     graph_.unmarkBlocks();

     return true;

 }

 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;

     }

     JS_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()->getOperand(0);

     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 = lhs.term->toPhi()->getOperand(1);

     if (lhsWrite->isBeta())

         lhsWrite = lhsWrite->getOperand(0);

     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 bound(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 (!bound.add(rhs, 1))

                 return nullptr;

         }

         if (!bound.add(lhsInitial, -1))

             return nullptr;

         int32_t lhsConstant;

         if (!SafeSub(0, lhs.constant, &lhsConstant))

             return nullptr;

         if (!bound.add(lhsConstant))

             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 (!bound.add(lhsInitial, 1))

             return nullptr;

         if (rhs) {

             if (!bound.add(rhs, -1))

                 return nullptr;

         }

         if (!bound.add(lhs.constant))

             return nullptr;

     } else {

         return nullptr;

     }

     return new(alloc()) LoopIterationBound(header, test, bound);

 }

 void

 RangeAnalysis::analyzeLoopPhi(MBasicBlock *header, 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.

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

     MBasicBlock *preLoop = header->loopPredecessor();

     JS_ASSERT(!preLoop->isMarked() && preLoop->successorWithPhis() == header);

     MBasicBlock *backedge = header->backedge();

     JS_ASSERT(backedge->isMarked() && backedge->successorWithPhis() == header);

     MDefinition *initial = phi->getOperand(preLoop->positionInPhiSuccessor());

     if (initial->block()->isMarked())

         return;

     SimpleLinearSum modified = ExtractLinearSum(phi->getOperand(backedge->positionInPhiSuccessor()));

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

         return;

     if (!phi->range())

         phi->setRange(new(alloc()) Range());

     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->sum);

     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));

     }

     IonSpew(IonSpew_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();

 }

 // Convert all components of a linear sum *except* its constant to a definition,

 // adding any necessary instructions to the end of block.

 static inline MDefinition *

 ConvertLinearSum(TempAllocator &alloc, MBasicBlock *block, const LinearSum &sum)

 {

     MDefinition *def = nullptr;

     for (size_t i = 0; i < sum.numTerms(); i++) {

         LinearTerm term = sum.term(i);

         JS_ASSERT(!term.term->isConstant());

         if (term.scale == 1) {

             if (def) {

                 def = MAdd::New(alloc, def, term.term);

                 def->toAdd()->setInt32();

                 block->insertBefore(block->lastIns(), def->toInstruction());

                 def->computeRange(alloc);

             } else {

                 def = term.term;

             }

         } else if (term.scale == -1) {

             if (!def) {

                 def = MConstant::New(alloc, Int32Value(0));

                 block->insertBefore(block->lastIns(), def->toInstruction());

                 def->computeRange(alloc);

             }

             def = MSub::New(alloc, def, term.term);

             def->toSub()->setInt32();

             block->insertBefore(block->lastIns(), def->toInstruction());

             def->computeRange(alloc);

         } else {

             JS_ASSERT(term.scale != 0);

             MConstant *factor = MConstant::New(alloc, Int32Value(term.scale));

             block->insertBefore(block->lastIns(), factor);

             MMul *mul = MMul::New(alloc, term.term, factor);

             mul->setInt32();

             block->insertBefore(block->lastIns(), mul);

             mul->computeRange(alloc);

             if (def) {

                 def = MAdd::New(alloc, def, mul);

                 def->toAdd()->setInt32();

                 block->insertBefore(block->lastIns(), def->toInstruction());

                 def->computeRange(alloc);

             } else {

                 def = mul;

             }

         }

     }

     if (!def) {

         def = MConstant::New(alloc, Int32Value(0));

         block->insertBefore(block->lastIns(), def->toInstruction());

         def->computeRange(alloc);

     }

     return def;

 }

 bool

 RangeAnalysis::tryHoistBoundsCheck(MBasicBlock *header, MBoundsCheck *ins)

 {

     // The bounds check's length must be loop invariant.

     if (ins->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();

     JS_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;

     MBoundsCheckLower *lowerCheck = MBoundsCheckLower::New(alloc(), lowerTerm);

     lowerCheck->setMinimum(lowerConstant);

     MBoundsCheck *upperCheck = MBoundsCheck::New(alloc(), upperTerm, ins->length());

     upperCheck->setMinimum(upperConstant);

     upperCheck->setMaximum(upperConstant);

     // Hoist the loop invariant upper and lower bounds checks.

     preLoop->insertBefore(preLoop->lastIns(), lowerCheck);

     preLoop->insertBefore(preLoop->lastIns(), upperCheck);

     return true;

 }

 bool

 RangeAnalysis::analyze()

 {

     IonSpew(IonSpew_Range, "Doing range propagation");

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

         MBasicBlock *block = *iter;

         if (block->unreachable())

             continue;

         for (MDefinitionIterator iter(block); iter; iter++) {

             MDefinition *def = *iter;

             def->computeRange(alloc());

             IonSpew(IonSpew_Range, "computing range on %d", def->id());

             SpewRange(def);

         }

         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();

             // Would have been nice to implement this using collectRangeInfoPreTrunc()

             // methods but it needs the minAsmJSHeapLength().

             if (mir->compilingAsmJS()) {

                 uint32_t minHeapLength = mir->minAsmJSHeapLength();

                 if (iter->isAsmJSLoadHeap()) {

                     MAsmJSLoadHeap *ins = iter->toAsmJSLoadHeap();

                     Range *range = ins->ptr()->range();

                     if (range && range->hasInt32LowerBound() && range->lower() >= 0 &&

                         range->hasInt32UpperBound() && (uint32_t) range->upper() < minHeapLength) {

                         ins->setSkipBoundsCheck(true);

                     }

                 } else if (iter->isAsmJSStoreHeap()) {

                     MAsmJSStoreHeap *ins = iter->toAsmJSStoreHeap();

                     Range *range = ins->ptr()->range();

                     if (range && range->hasInt32LowerBound() && range->lower() >= 0 &&

                         range->hasInt32UpperBound() && (uint32_t) range->upper() < minHeapLength) {

                         ins->setSkipBoundsCheck(true);

                     }

                 }

             }

         }

     }

     return true;

 }

 bool

 RangeAnalysis::addRangeAssertions()

 {

     if (!js_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;

         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;

             }

             Range r(ins);

             // Don't insert assertions if there's nothing interesting to assert.

             if (r.isUnknown() || (ins->type() == MIRType_Int32 && r.isUnknownInt32()))

                 continue;

             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.

             MInstructionIterator insertIter = ins->isPhi()

                                             ? block->begin()

                                             : block->begin(ins->toInstruction());

             while (insertIter->isBeta() ||

                    insertIter->isInterruptCheck() ||

                    insertIter->isInterruptCheckPar() ||

                    insertIter->isConstant())

             {

                 insertIter++;

             }

             if (*insertIter == *iter)

                 block->insertAfter(*insertIter,  guard);

             else

                 block->insertBefore(*insertIter, 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()) {

         canHaveFractionalPart_ = false;

         // Clearing the fractional field may provide an opportunity to refine

         // lower_ or upper_.

         refineInt32BoundsByExponent(max_exponent_, &lower_, &upper_);

         assertInvariants();

     }

 }

 void

 Range::wrapAroundToShiftCount()

 {

     wrapAroundToInt32();

     if (lower() < 0 || upper() >= 32)

         setInt32(0, 31);

 }

 void

 Range::wrapAroundToBoolean()

 {

     wrapAroundToInt32();

     if (!isBoolean())

         setInt32(0, 1);

 }

 bool

 MDefinition::truncate()

 {

     // No procedure defined for truncating this instruction.

     return false;

 }

 bool

 MConstant::truncate()

 {

     if (!value_.isDouble())

         return false;

     // Truncate the double to int, since all uses truncates it.

     int32_t res = ToInt32(value_.toDouble());

     value_.setInt32(res);

     setResultType(MIRType_Int32);

     if (range())

         range()->setInt32(res, res);

     return true;

 }

 bool

 MAdd::truncate()

 {

     // Remember analysis, needed for fallible checks.

     setTruncated(true);

     if (type() == MIRType_Double || type() == MIRType_Int32) {

         specialization_ = MIRType_Int32;

         setResultType(MIRType_Int32);

         if (range())

             range()->wrapAroundToInt32();

         return true;

     }

     return false;

 }

 bool

 MSub::truncate()

 {

     // Remember analysis, needed for fallible checks.

     setTruncated(true);

     if (type() == MIRType_Double || type() == MIRType_Int32) {

         specialization_ = MIRType_Int32;

         setResultType(MIRType_Int32);

         if (range())

             range()->wrapAroundToInt32();

         return true;

     }

     return false;

 }

 bool

 MMul::truncate()

 {

     // Remember analysis, needed to remove negative zero checks.

     setTruncated(true);

     if (type() == MIRType_Double || type() == MIRType_Int32) {

         specialization_ = MIRType_Int32;

         setResultType(MIRType_Int32);

         setCanBeNegativeZero(false);

         if (range())

             range()->wrapAroundToInt32();

         return true;

     }

     return false;

 }

 bool

 MDiv::truncate()

 {

     // Remember analysis, needed to remove negative zero checks.

     setTruncatedIndirectly(true);

     // Check if this division only flows in bitwise instructions.

     if (!isTruncated()) {

         bool allUsesExplictlyTruncate = true;

         for (MUseDefIterator use(this); allUsesExplictlyTruncate && use; use++) {

             switch (use.def()->op()) {

               case MDefinition::Op_BitAnd:

               case MDefinition::Op_BitOr:

               case MDefinition::Op_BitXor:

               case MDefinition::Op_Lsh:

               case MDefinition::Op_Rsh:

               case MDefinition::Op_Ursh:

                 break;

               default:

                 allUsesExplictlyTruncate = false;

             }

         }

         if (allUsesExplictlyTruncate)

             setTruncated(true);

     }

     // Divisions where the lhs and rhs are unsigned and the result is

     // truncated can be lowered more efficiently.

     if (specialization() == MIRType_Int32 && tryUseUnsignedOperands()) {

         unsigned_ = true;

         return true;

     }

     // No modifications.

     return false;

 }

 bool

 MMod::truncate()

 {

     // Remember analysis, needed to remove negative zero checks.

     setTruncated(true);

     // As for division, handle unsigned modulus with a truncated result.

     if (specialization() == MIRType_Int32 && tryUseUnsignedOperands()) {

         unsigned_ = true;

         return true;

     }

     // No modifications.

     return false;

 }

 bool

 MToDouble::truncate()

 {

     JS_ASSERT(type() == MIRType_Double);

     // We use the return type to flag that this MToDouble should be replaced by

     // a MTruncateToInt32 when modifying the graph.

     setResultType(MIRType_Int32);

     if (range())

         range()->wrapAroundToInt32();

     return true;

 }

 bool

 MLoadTypedArrayElementStatic::truncate()

 {

     setInfallible();

     return false;

 }

 bool

 MDefinition::isOperandTruncated(size_t index) const

 {

     return false;

 }

 bool

 MTruncateToInt32::isOperandTruncated(size_t index) const

 {

     return true;

 }

 bool

 MBinaryBitwiseInstruction::isOperandTruncated(size_t index) const

 {

     return true;

 }

 bool

 MAdd::isOperandTruncated(size_t index) const

 {

     return isTruncated();

 }

 bool

 MSub::isOperandTruncated(size_t index) const

 {

     return isTruncated();

 }

 bool

 MMul::isOperandTruncated(size_t index) const

 {

     return isTruncated();

 }

 bool

 MToDouble::isOperandTruncated(size_t index) const

 {

     // The return type is used to flag that we are replacing this Double by a

     // Truncate of its operand if needed.

     return type() == MIRType_Int32;

 }

 bool

 MStoreTypedArrayElement::isOperandTruncated(size_t index) const

 {

     return index == 2 && !isFloatArray();

 }

 bool

 MStoreTypedArrayElementHole::isOperandTruncated(size_t index) const

 {

     return index == 3 && !isFloatArray();

 }

 bool

 MStoreTypedArrayElementStatic::isOperandTruncated(size_t index) const

 {

     return index == 1 && !isFloatArray();

 }

 bool

 MCompare::truncate()

 {

     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;

     compareType_ = Compare_Int32;

     // Truncating the operands won't change their value, but it will change

     // their type, which we need because we now expect integer inputs.

     truncateOperands_ = true;

     return true;

 }

 bool

 MCompare::isOperandTruncated(size_t index) const

 {

     // If we're doing an int32 comparison on operands which were previously

     // floating-point, convert them!

     JS_ASSERT_IF(truncateOperands_, isInt32Comparison());

     return truncateOperands_;

 }

 // Ensure that all observables uses can work with a truncated

 // version of the |candidate|'s result.

 static bool

 AllUsesTruncate(MInstruction *candidate)

 {

     // 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();

     for (MUseIterator use(candidate->usesBegin()); use != candidate->usesEnd(); use++) {

         if (!use->consumer()->isDefinition()) {

             // We can only skip testing resume points, if all original uses are

             // still present, or if the value does not need conversion.

             // Otherwise a branch removed by UCE might rely on the non-truncated

             // value, and any bailout with a truncated value might lead an

             // incorrect value.

             if (candidate->isUseRemoved() && needsConversion)

                 return false;

             continue;

         }

         if (!use->consumer()->toDefinition()->isOperandTruncated(use->index()))

             return false;

     }

     return true;

 }

 static bool

 CanTruncate(MInstruction *candidate)

 {

     // 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 true;

     // 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: the result of a/b can be infinite

     // but cannot actually have rounding errors induced by truncation.

     if (candidate->isDiv() && candidate->toDiv()->specialization() == MIRType_Int32)

         canHaveRoundingErrors = false;

     if (canHaveRoundingErrors)

         return false;

     // Ensure all observable uses are truncated.

     return AllUsesTruncate(candidate);

 }

 static void

 RemoveTruncatesOnOutput(MInstruction *truncated)

 {

     // Compare returns a boolean so it doen't have any output truncates.

     if (truncated->isCompare())

         return;

     JS_ASSERT(truncated->type() == MIRType_Int32);

     JS_ASSERT(Range(truncated).isInt32());

     for (MUseDefIterator use(truncated); use; use++) {

         MDefinition *def = use.def();

         if (!def->isTruncateToInt32() || !def->isToInt32())

             continue;

         def->replaceAllUsesWith(truncated);

     }

 }

 static void

 AdjustTruncatedInputs(TempAllocator &alloc, MInstruction *truncated)

 {

     MBasicBlock *block = truncated->block();

     for (size_t i = 0, e = truncated->numOperands(); i < e; i++) {

         if (!truncated->isOperandTruncated(i))

             continue;

         MDefinition *input = truncated->getOperand(i);

         if (input->type() == MIRType_Int32)

             continue;

         if (input->isToDouble() && input->getOperand(0)->type() == MIRType_Int32) {

             JS_ASSERT(input->range()->isInt32());

             truncated->replaceOperand(i, input->getOperand(0));

         } else {

             MTruncateToInt32 *op = MTruncateToInt32::New(alloc, truncated->getOperand(i));

             block->insertBefore(truncated, op);

             truncated->replaceOperand(i, op);

         }

     }

     if (truncated->isToDouble()) {

         truncated->replaceAllUsesWith(truncated->getOperand(0));

         block->discard(truncated);

     }

 }

 // 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()

 {

     IonSpew(IonSpew_Range, "Do range-base truncation (backward loop)");

     Vector<MInstruction *, 16, SystemAllocPolicy> worklist;

     Vector<MBinaryBitwiseInstruction *, 16, SystemAllocPolicy> bitops;

     for (PostorderIterator block(graph_.poBegin()); block != graph_.poEnd(); block++) {

         for (MInstructionReverseIterator iter(block->rbegin()); iter != block->rend(); iter++) {

             if (iter->type() == MIRType_None)

                 continue;

             // Remember all bitop instructions for folding after range analysis.

             switch (iter->op()) {

               case MDefinition::Op_BitAnd:

               case MDefinition::Op_BitOr:

               case MDefinition::Op_BitXor:

               case MDefinition::Op_Lsh:

               case MDefinition::Op_Rsh:

               case MDefinition::Op_Ursh:

                 if (!bitops.append(static_cast<MBinaryBitwiseInstruction*>(*iter)))

                     return false;

               default:;

             }

             if (!CanTruncate(*iter))

                 continue;

             // Truncate this instruction if possible.

             if (!iter->truncate())

                 continue;

             // 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.

     IonSpew(IonSpew_Range, "Do graph type fixup (dequeue)");

     while (!worklist.empty()) {

         MInstruction *ins = worklist.popCopy();

         ins->setNotInWorklist();

         RemoveTruncatesOnOutput(ins);

         AdjustTruncatedInputs(alloc(), ins);

     }

     // 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];

         MDefinition *folded = ins->foldUnnecessaryBitop();

         if (folded != ins)

             ins->replaceAllUsesWith(folded);

     }

     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;

 }

 void

 MDiv::collectRangeInfoPreTrunc()

 {

     Range lhsRange(lhs());

     if (lhsRange.isFiniteNonNegative())

         canBeNegativeDividend_ = false;

 }

 void

 MMod::collectRangeInfoPreTrunc()

 {

     Range lhsRange(lhs());

     if (lhsRange.isFiniteNonNegative())

         canBeNegativeDividend_ = 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(operand()).canBeNaN())

         operandIsNeverNaN_ = true;

 }

 void

 MPowHalf::collectRangeInfoPreTrunc()

 {

     Range inputRange(input());

     if (!inputRange.canBeInfiniteOrNaN() || inputRange.hasInt32LowerBound())

         operandIsNeverNegativeInfinity_ = true;

     if (!inputRange.canBeZero())

         operandIsNeverNegativeZero_ = true;

     if (!inputRange.canBeNaN())

         operandIsNeverNaN_ = true;

 }

 void

 MUrsh::collectRangeInfoPreTrunc()

 {

     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;

 }

 bool

 RangeAnalysis::prepareForUCE(bool *shouldRemoveDeadCode)

 {

     *shouldRemoveDeadCode = false;

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