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 /*

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  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

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  * This code is free software; you can redistribute it and/or modify it

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  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

  * version 2 for more details (a copy is included in the LICENSE file that

  * accompanied this code).

  *

  * You should have received a copy of the GNU General Public License version

  * 2 along with this work; if not, write to the Free Software Foundation,

  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

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  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

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 // Portions of code courtesy of Clifford Click

 // Optimization - Graph Style

 #include "incls/_precompiled.incl"

 #include "incls/_divnode.cpp.incl"

 #include <math.h>

 //----------------------magic_int_divide_constants-----------------------------

 // Compute magic multiplier and shift constant for converting a 32 bit divide

 // by constant into a multiply/shift/add series. Return false if calculations

 // fail.

 //

 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with

 // minor type name and parameter changes.

 static bool magic_int_divide_constants(jint d, jint &M, jint &s) {

   int32_t p;

   uint32_t ad, anc, delta, q1, r1, q2, r2, t;

   const uint32_t two31 = 0x80000000L;     // 2**31.

   ad = ABS(d);

   if (d == 0 || d == 1) return false;

   t = two31 + ((uint32_t)d >> 31);

   anc = t - 1 - t%ad;     // Absolute value of nc.

   p = 31;                 // Init. p.

   q1 = two31/anc;         // Init. q1 = 2**p/|nc|.

   r1 = two31 - q1*anc;    // Init. r1 = rem(2**p, |nc|).

   q2 = two31/ad;          // Init. q2 = 2**p/|d|.

   r2 = two31 - q2*ad;     // Init. r2 = rem(2**p, |d|).

   do {

     p = p + 1;

     q1 = 2*q1;            // Update q1 = 2**p/|nc|.

     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).

     if (r1 >= anc) {      // (Must be an unsigned

       q1 = q1 + 1;        // comparison here).

       r1 = r1 - anc;

     }

     q2 = 2*q2;            // Update q2 = 2**p/|d|.

     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).

     if (r2 >= ad) {       // (Must be an unsigned

       q2 = q2 + 1;        // comparison here).

       r2 = r2 - ad;

     }

     delta = ad - r2;

   } while (q1 < delta || (q1 == delta && r1 == 0));

   M = q2 + 1;

   if (d < 0) M = -M;      // Magic number and

   s = p - 32;             // shift amount to return.

   return true;

 }

 //--------------------------transform_int_divide-------------------------------

 // Convert a division by constant divisor into an alternate Ideal graph.

 // Return NULL if no transformation occurs.

 static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) {

   // Check for invalid divisors

   assert( divisor != 0 && divisor != min_jint,

           "bad divisor for transforming to long multiply" );

   bool d_pos = divisor >= 0;

   jint d = d_pos ? divisor : -divisor;

   const int N = 32;

   // Result

   Node *q = NULL;

   if (d == 1) {

     // division by +/- 1

     if (!d_pos) {

       // Just negate the value

       q = new (phase->C, 3) SubINode(phase->intcon(0), dividend);

     }

   } else if ( is_power_of_2(d) ) {

     // division by +/- a power of 2

     // See if we can simply do a shift without rounding

     bool needs_rounding = true;

     const Type *dt = phase->type(dividend);

     const TypeInt *dti = dt->isa_int();

     if (dti && dti->_lo >= 0) {

       // we don't need to round a positive dividend

       needs_rounding = false;

     } else if( dividend->Opcode() == Op_AndI ) {

       // An AND mask of sufficient size clears the low bits and

       // I can avoid rounding.

       const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int();

       if( andconi_t && andconi_t->is_con() ) {

         jint andconi = andconi_t->get_con();

         if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) {

           if( (-andconi) == d ) // Remove AND if it clears bits which will be shifted

             dividend = dividend->in(1);

           needs_rounding = false;

         }

       }

     }

     // Add rounding to the shift to handle the sign bit

     int l = log2_intptr(d-1)+1;

     if (needs_rounding) {

       // Divide-by-power-of-2 can be made into a shift, but you have to do

       // more math for the rounding.  You need to add 0 for positive

       // numbers, and "i-1" for negative numbers.  Example: i=4, so the

       // shift is by 2.  You need to add 3 to negative dividends and 0 to

       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,

       // (-2+3)>>2 becomes 0, etc.

       // Compute 0 or -1, based on sign bit

       Node *sign = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N - 1)));

       // Mask sign bit to the low sign bits

       Node *round = phase->transform(new (phase->C, 3) URShiftINode(sign, phase->intcon(N - l)));

       // Round up before shifting

       dividend = phase->transform(new (phase->C, 3) AddINode(dividend, round));

     }

     // Shift for division

     q = new (phase->C, 3) RShiftINode(dividend, phase->intcon(l));

     if (!d_pos) {

       q = new (phase->C, 3) SubINode(phase->intcon(0), phase->transform(q));

     }

   } else {

     // Attempt the jint constant divide -> multiply transform found in

     //   "Division by Invariant Integers using Multiplication"

     //     by Granlund and Montgomery

     // See also "Hacker's Delight", chapter 10 by Warren.

     jint magic_const;

     jint shift_const;

     if (magic_int_divide_constants(d, magic_const, shift_const)) {

       Node *magic = phase->longcon(magic_const);

       Node *dividend_long = phase->transform(new (phase->C, 2) ConvI2LNode(dividend));

       // Compute the high half of the dividend x magic multiplication

       Node *mul_hi = phase->transform(new (phase->C, 3) MulLNode(dividend_long, magic));

       if (magic_const < 0) {

         mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(N)));

         mul_hi = phase->transform(new (phase->C, 2) ConvL2INode(mul_hi));

         // The magic multiplier is too large for a 32 bit constant. We've adjusted

         // it down by 2^32, but have to add 1 dividend back in after the multiplication.

         // This handles the "overflow" case described by Granlund and Montgomery.

         mul_hi = phase->transform(new (phase->C, 3) AddINode(dividend, mul_hi));

         // Shift over the (adjusted) mulhi

         if (shift_const != 0) {

           mul_hi = phase->transform(new (phase->C, 3) RShiftINode(mul_hi, phase->intcon(shift_const)));

         }

       } else {

         // No add is required, we can merge the shifts together.

         mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(N + shift_const)));

         mul_hi = phase->transform(new (phase->C, 2) ConvL2INode(mul_hi));

       }

       // Get a 0 or -1 from the sign of the dividend.

       Node *addend0 = mul_hi;

       Node *addend1 = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N-1)));

       // If the divisor is negative, swap the order of the input addends;

       // this has the effect of negating the quotient.

       if (!d_pos) {

         Node *temp = addend0; addend0 = addend1; addend1 = temp;

       }

       // Adjust the final quotient by subtracting -1 (adding 1)

       // from the mul_hi.

       q = new (phase->C, 3) SubINode(addend0, addend1);

     }

   }

   return q;

 }

 //---------------------magic_long_divide_constants-----------------------------

 // Compute magic multiplier and shift constant for converting a 64 bit divide

 // by constant into a multiply/shift/add series. Return false if calculations

 // fail.

 //

 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with

 // minor type name and parameter changes.  Adjusted to 64 bit word width.

 static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) {

   int64_t p;

   uint64_t ad, anc, delta, q1, r1, q2, r2, t;

   const uint64_t two63 = 0x8000000000000000LL;     // 2**63.

   ad = ABS(d);

   if (d == 0 || d == 1) return false;

   t = two63 + ((uint64_t)d >> 63);

   anc = t - 1 - t%ad;     // Absolute value of nc.

   p = 63;                 // Init. p.

   q1 = two63/anc;         // Init. q1 = 2**p/|nc|.

   r1 = two63 - q1*anc;    // Init. r1 = rem(2**p, |nc|).

   q2 = two63/ad;          // Init. q2 = 2**p/|d|.

   r2 = two63 - q2*ad;     // Init. r2 = rem(2**p, |d|).

   do {

     p = p + 1;

     q1 = 2*q1;            // Update q1 = 2**p/|nc|.

     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).

     if (r1 >= anc) {      // (Must be an unsigned

       q1 = q1 + 1;        // comparison here).

       r1 = r1 - anc;

     }

     q2 = 2*q2;            // Update q2 = 2**p/|d|.

     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).

     if (r2 >= ad) {       // (Must be an unsigned

       q2 = q2 + 1;        // comparison here).

       r2 = r2 - ad;

     }

     delta = ad - r2;

   } while (q1 < delta || (q1 == delta && r1 == 0));

   M = q2 + 1;

   if (d < 0) M = -M;      // Magic number and

   s = p - 64;             // shift amount to return.

   return true;

 }

 //---------------------long_by_long_mulhi--------------------------------------

 // Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication

 static Node* long_by_long_mulhi(PhaseGVN* phase, Node* dividend, jlong magic_const) {

   // If the architecture supports a 64x64 mulhi, there is

   // no need to synthesize it in ideal nodes.

   if (Matcher::has_match_rule(Op_MulHiL)) {

     Node* v = phase->longcon(magic_const);

     return new (phase->C, 3) MulHiLNode(dividend, v);

   }

   // Taken from Hacker's Delight, Fig. 8-2. Multiply high signed.

   // (http://www.hackersdelight.org/HDcode/mulhs.c)

   //

   // int mulhs(int u, int v) {

   //    unsigned u0, v0, w0;

   //    int u1, v1, w1, w2, t;

   //

   //    u0 = u & 0xFFFF;  u1 = u >> 16;

   //    v0 = v & 0xFFFF;  v1 = v >> 16;

   //    w0 = u0*v0;

   //    t  = u1*v0 + (w0 >> 16);

   //    w1 = t & 0xFFFF;

   //    w2 = t >> 16;

   //    w1 = u0*v1 + w1;

   //    return u1*v1 + w2 + (w1 >> 16);

   // }

   //

   // Note: The version above is for 32x32 multiplications, while the

   // following inline comments are adapted to 64x64.

   const int N = 64;

   // u0 = u & 0xFFFFFFFF;  u1 = u >> 32;

   Node* u0 = phase->transform(new (phase->C, 3) AndLNode(dividend, phase->longcon(0xFFFFFFFF)));

   Node* u1 = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N / 2)));

   // v0 = v & 0xFFFFFFFF;  v1 = v >> 32;

   Node* v0 = phase->longcon(magic_const & 0xFFFFFFFF);

   Node* v1 = phase->longcon(magic_const >> (N / 2));

   // w0 = u0*v0;

   Node* w0 = phase->transform(new (phase->C, 3) MulLNode(u0, v0));

   // t = u1*v0 + (w0 >> 32);

   Node* u1v0 = phase->transform(new (phase->C, 3) MulLNode(u1, v0));

   Node* temp = phase->transform(new (phase->C, 3) URShiftLNode(w0, phase->intcon(N / 2)));

   Node* t    = phase->transform(new (phase->C, 3) AddLNode(u1v0, temp));

   // w1 = t & 0xFFFFFFFF;

   Node* w1 = new (phase->C, 3) AndLNode(t, phase->longcon(0xFFFFFFFF));

   // w2 = t >> 32;

   Node* w2 = new (phase->C, 3) RShiftLNode(t, phase->intcon(N / 2));

   // 6732154: Construct both w1 and w2 before transforming, so t

   // doesn't go dead prematurely.

   // 6837011: We need to transform w2 before w1 because the

   // transformation of w1 could return t.

   w2 = phase->transform(w2);

   w1 = phase->transform(w1);

   // w1 = u0*v1 + w1;

   Node* u0v1 = phase->transform(new (phase->C, 3) MulLNode(u0, v1));

   w1         = phase->transform(new (phase->C, 3) AddLNode(u0v1, w1));

   // return u1*v1 + w2 + (w1 >> 32);

   Node* u1v1  = phase->transform(new (phase->C, 3) MulLNode(u1, v1));

   Node* temp1 = phase->transform(new (phase->C, 3) AddLNode(u1v1, w2));

   Node* temp2 = phase->transform(new (phase->C, 3) RShiftLNode(w1, phase->intcon(N / 2)));

   return new (phase->C, 3) AddLNode(temp1, temp2);

 }

 //--------------------------transform_long_divide------------------------------

 // Convert a division by constant divisor into an alternate Ideal graph.

 // Return NULL if no transformation occurs.

 static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {

   // Check for invalid divisors

   assert( divisor != 0L && divisor != min_jlong,

           "bad divisor for transforming to long multiply" );

   bool d_pos = divisor >= 0;

   jlong d = d_pos ? divisor : -divisor;

   const int N = 64;

   // Result

   Node *q = NULL;

   if (d == 1) {

     // division by +/- 1

     if (!d_pos) {

       // Just negate the value

       q = new (phase->C, 3) SubLNode(phase->longcon(0), dividend);

     }

   } else if ( is_power_of_2_long(d) ) {

     // division by +/- a power of 2

     // See if we can simply do a shift without rounding

     bool needs_rounding = true;

     const Type *dt = phase->type(dividend);

     const TypeLong *dtl = dt->isa_long();

     if (dtl && dtl->_lo > 0) {

       // we don't need to round a positive dividend

       needs_rounding = false;

     } else if( dividend->Opcode() == Op_AndL ) {

       // An AND mask of sufficient size clears the low bits and

       // I can avoid rounding.

       const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();

       if( andconl_t && andconl_t->is_con() ) {

         jlong andconl = andconl_t->get_con();

         if( andconl < 0 && is_power_of_2_long(-andconl) && (-andconl) >= d ) {

           if( (-andconl) == d ) // Remove AND if it clears bits which will be shifted

             dividend = dividend->in(1);

           needs_rounding = false;

         }

       }

     }

     // Add rounding to the shift to handle the sign bit

     int l = log2_long(d-1)+1;

     if (needs_rounding) {

       // Divide-by-power-of-2 can be made into a shift, but you have to do

       // more math for the rounding.  You need to add 0 for positive

       // numbers, and "i-1" for negative numbers.  Example: i=4, so the

       // shift is by 2.  You need to add 3 to negative dividends and 0 to

       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,

       // (-2+3)>>2 becomes 0, etc.

       // Compute 0 or -1, based on sign bit

       Node *sign = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N - 1)));

       // Mask sign bit to the low sign bits

       Node *round = phase->transform(new (phase->C, 3) URShiftLNode(sign, phase->intcon(N - l)));

       // Round up before shifting

       dividend = phase->transform(new (phase->C, 3) AddLNode(dividend, round));

     }

     // Shift for division

     q = new (phase->C, 3) RShiftLNode(dividend, phase->intcon(l));

     if (!d_pos) {

       q = new (phase->C, 3) SubLNode(phase->longcon(0), phase->transform(q));

     }

   } else if ( !Matcher::use_asm_for_ldiv_by_con(d) ) { // Use hardware DIV instruction when

                                                        // it is faster than code generated below.

     // Attempt the jlong constant divide -> multiply transform found in

     //   "Division by Invariant Integers using Multiplication"

     //     by Granlund and Montgomery

     // See also "Hacker's Delight", chapter 10 by Warren.

     jlong magic_const;

     jint shift_const;

     if (magic_long_divide_constants(d, magic_const, shift_const)) {

       // Compute the high half of the dividend x magic multiplication

       Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));

       // The high half of the 128-bit multiply is computed.

       if (magic_const < 0) {

         // The magic multiplier is too large for a 64 bit constant. We've adjusted

         // it down by 2^64, but have to add 1 dividend back in after the multiplication.

         // This handles the "overflow" case described by Granlund and Montgomery.

         mul_hi = phase->transform(new (phase->C, 3) AddLNode(dividend, mul_hi));

       }

       // Shift over the (adjusted) mulhi

       if (shift_const != 0) {

         mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(shift_const)));

       }

       // Get a 0 or -1 from the sign of the dividend.

       Node *addend0 = mul_hi;

       Node *addend1 = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N-1)));

       // If the divisor is negative, swap the order of the input addends;

       // this has the effect of negating the quotient.

       if (!d_pos) {

         Node *temp = addend0; addend0 = addend1; addend1 = temp;

       }

       // Adjust the final quotient by subtracting -1 (adding 1)

       // from the mul_hi.

       q = new (phase->C, 3) SubLNode(addend0, addend1);

     }

   }

   return q;

 }

 //=============================================================================

 //------------------------------Identity---------------------------------------

 // If the divisor is 1, we are an identity on the dividend.

 Node *DivINode::Identity( PhaseTransform *phase ) {

   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;

 }

 //------------------------------Idealize---------------------------------------

 // Divides can be changed to multiplies and/or shifts

 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {

   if (in(0) && remove_dead_region(phase, can_reshape))  return this;

   // Don't bother trying to transform a dead node

   if( in(0) && in(0)->is_top() )  return NULL;

   const Type *t = phase->type( in(2) );

   if( t == TypeInt::ONE )       // Identity?

     return NULL;                // Skip it

   const TypeInt *ti = t->isa_int();

   if( !ti ) return NULL;

   if( !ti->is_con() ) return NULL;

   jint i = ti->get_con();       // Get divisor

   if (i == 0) return NULL;      // Dividing by zero constant does not idealize

   set_req(0,NULL);              // Dividing by a not-zero constant; no faulting

   // Dividing by MININT does not optimize as a power-of-2 shift.

   if( i == min_jint ) return NULL;

   return transform_int_divide( phase, in(1), i );

 }

 //------------------------------Value------------------------------------------

 // A DivINode divides its inputs.  The third input is a Control input, used to

 // prevent hoisting the divide above an unsafe test.

 const Type *DivINode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // x/x == 1 since we always generate the dynamic divisor check for 0.

   if( phase->eqv( in(1), in(2) ) )

     return TypeInt::ONE;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   // Divide the two numbers.  We approximate.

   // If divisor is a constant and not zero

   const TypeInt *i1 = t1->is_int();

   const TypeInt *i2 = t2->is_int();

   int widen = MAX2(i1->_widen, i2->_widen);

   if( i2->is_con() && i2->get_con() != 0 ) {

     int32 d = i2->get_con(); // Divisor

     jint lo, hi;

     if( d >= 0 ) {

       lo = i1->_lo/d;

       hi = i1->_hi/d;

     } else {

       if( d == -1 && i1->_lo == min_jint ) {

         // 'min_jint/-1' throws arithmetic exception during compilation

         lo = min_jint;

         // do not support holes, 'hi' must go to either min_jint or max_jint:

         // [min_jint, -10]/[-1,-1] ==> [min_jint] UNION [10,max_jint]

         hi = i1->_hi == min_jint ? min_jint : max_jint;

       } else {

         lo = i1->_hi/d;

         hi = i1->_lo/d;

       }

     }

     return TypeInt::make(lo, hi, widen);

   }

   // If the dividend is a constant

   if( i1->is_con() ) {

     int32 d = i1->get_con();

     if( d < 0 ) {

       if( d == min_jint ) {

         //  (-min_jint) == min_jint == (min_jint / -1)

         return TypeInt::make(min_jint, max_jint/2 + 1, widen);

       } else {

         return TypeInt::make(d, -d, widen);

       }

     }

     return TypeInt::make(-d, d, widen);

   }

   // Otherwise we give up all hope

   return TypeInt::INT;

 }

 //=============================================================================

 //------------------------------Identity---------------------------------------

 // If the divisor is 1, we are an identity on the dividend.

 Node *DivLNode::Identity( PhaseTransform *phase ) {

   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;

 }

 //------------------------------Idealize---------------------------------------

 // Dividing by a power of 2 is a shift.

 Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) {

   if (in(0) && remove_dead_region(phase, can_reshape))  return this;

   // Don't bother trying to transform a dead node

   if( in(0) && in(0)->is_top() )  return NULL;

   const Type *t = phase->type( in(2) );

   if( t == TypeLong::ONE )      // Identity?

     return NULL;                // Skip it

   const TypeLong *tl = t->isa_long();

   if( !tl ) return NULL;

   if( !tl->is_con() ) return NULL;

   jlong l = tl->get_con();      // Get divisor

   if (l == 0) return NULL;      // Dividing by zero constant does not idealize

   set_req(0,NULL);              // Dividing by a not-zero constant; no faulting

   // Dividing by MINLONG does not optimize as a power-of-2 shift.

   if( l == min_jlong ) return NULL;

   return transform_long_divide( phase, in(1), l );

 }

 //------------------------------Value------------------------------------------

 // A DivLNode divides its inputs.  The third input is a Control input, used to

 // prevent hoisting the divide above an unsafe test.

 const Type *DivLNode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // x/x == 1 since we always generate the dynamic divisor check for 0.

   if( phase->eqv( in(1), in(2) ) )

     return TypeLong::ONE;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   // Divide the two numbers.  We approximate.

   // If divisor is a constant and not zero

   const TypeLong *i1 = t1->is_long();

   const TypeLong *i2 = t2->is_long();

   int widen = MAX2(i1->_widen, i2->_widen);

   if( i2->is_con() && i2->get_con() != 0 ) {

     jlong d = i2->get_con();    // Divisor

     jlong lo, hi;

     if( d >= 0 ) {

       lo = i1->_lo/d;

       hi = i1->_hi/d;

     } else {

       if( d == CONST64(-1) && i1->_lo == min_jlong ) {

         // 'min_jlong/-1' throws arithmetic exception during compilation

         lo = min_jlong;

         // do not support holes, 'hi' must go to either min_jlong or max_jlong:

         // [min_jlong, -10]/[-1,-1] ==> [min_jlong] UNION [10,max_jlong]

         hi = i1->_hi == min_jlong ? min_jlong : max_jlong;

       } else {

         lo = i1->_hi/d;

         hi = i1->_lo/d;

       }

     }

     return TypeLong::make(lo, hi, widen);

   }

   // If the dividend is a constant

   if( i1->is_con() ) {

     jlong d = i1->get_con();

     if( d < 0 ) {

       if( d == min_jlong ) {

         //  (-min_jlong) == min_jlong == (min_jlong / -1)

         return TypeLong::make(min_jlong, max_jlong/2 + 1, widen);

       } else {

         return TypeLong::make(d, -d, widen);

       }

     }

     return TypeLong::make(-d, d, widen);

   }

   // Otherwise we give up all hope

   return TypeLong::LONG;

 }

 //=============================================================================

 //------------------------------Value------------------------------------------

 // An DivFNode divides its inputs.  The third input is a Control input, used to

 // prevent hoisting the divide above an unsafe test.

 const Type *DivFNode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   // x/x == 1, we ignore 0/0.

   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)

   // Does not work for variables because of NaN's

   if( phase->eqv( in(1), in(2) ) && t1->base() == Type::FloatCon)

     if (!g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) // could be negative ZERO or NaN

       return TypeF::ONE;

   if( t2 == TypeF::ONE )

     return t1;

   // If divisor is a constant and not zero, divide them numbers

   if( t1->base() == Type::FloatCon &&

       t2->base() == Type::FloatCon &&

       t2->getf() != 0.0 ) // could be negative zero

     return TypeF::make( t1->getf()/t2->getf() );

   // If the dividend is a constant zero

   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)

   // Test TypeF::ZERO is not sufficient as it could be negative zero

   if( t1 == TypeF::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0 )

     return TypeF::ZERO;

   // Otherwise we give up all hope

   return Type::FLOAT;

 }

 //------------------------------isA_Copy---------------------------------------

 // Dividing by self is 1.

 // If the divisor is 1, we are an identity on the dividend.

 Node *DivFNode::Identity( PhaseTransform *phase ) {

   return (phase->type( in(2) ) == TypeF::ONE) ? in(1) : this;

 }

 //------------------------------Idealize---------------------------------------

 Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) {

   if (in(0) && remove_dead_region(phase, can_reshape))  return this;

   // Don't bother trying to transform a dead node

   if( in(0) && in(0)->is_top() )  return NULL;

   const Type *t2 = phase->type( in(2) );

   if( t2 == TypeF::ONE )         // Identity?

     return NULL;                // Skip it

   const TypeF *tf = t2->isa_float_constant();

   if( !tf ) return NULL;

   if( tf->base() != Type::FloatCon ) return NULL;

   // Check for out of range values

   if( tf->is_nan() || !tf->is_finite() ) return NULL;

   // Get the value

   float f = tf->getf();

   int exp;

   // Only for special case of dividing by a power of 2

   if( frexp((double)f, &exp) != 0.5 ) return NULL;

   // Limit the range of acceptable exponents

   if( exp < -126 || exp > 126 ) return NULL;

   // Compute the reciprocal

   float reciprocal = ((float)1.0) / f;

   assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );

   // return multiplication by the reciprocal

   return (new (phase->C, 3) MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));

 }

 //=============================================================================

 //------------------------------Value------------------------------------------

 // An DivDNode divides its inputs.  The third input is a Control input, used to

 // prevent hoisting the divide above an unsafe test.

 const Type *DivDNode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   // x/x == 1, we ignore 0/0.

   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)

   // Does not work for variables because of NaN's

   if( phase->eqv( in(1), in(2) ) && t1->base() == Type::DoubleCon)

     if (!g_isnan(t1->getd()) && g_isfinite(t1->getd()) && t1->getd() != 0.0) // could be negative ZERO or NaN

       return TypeD::ONE;

   if( t2 == TypeD::ONE )

     return t1;

 #if defined(IA32)

   if (!phase->C->method()->is_strict())

     // Can't trust native compilers to properly fold strict double

     // division with round-to-zero on this platform.

 #endif

     {

       // If divisor is a constant and not zero, divide them numbers

       if( t1->base() == Type::DoubleCon &&

           t2->base() == Type::DoubleCon &&

           t2->getd() != 0.0 ) // could be negative zero

         return TypeD::make( t1->getd()/t2->getd() );

     }

   // If the dividend is a constant zero

   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)

   // Test TypeF::ZERO is not sufficient as it could be negative zero

   if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )

     return TypeD::ZERO;

   // Otherwise we give up all hope

   return Type::DOUBLE;

 }

 //------------------------------isA_Copy---------------------------------------

 // Dividing by self is 1.

 // If the divisor is 1, we are an identity on the dividend.

 Node *DivDNode::Identity( PhaseTransform *phase ) {

   return (phase->type( in(2) ) == TypeD::ONE) ? in(1) : this;

 }

 //------------------------------Idealize---------------------------------------

 Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) {

   if (in(0) && remove_dead_region(phase, can_reshape))  return this;

   // Don't bother trying to transform a dead node

   if( in(0) && in(0)->is_top() )  return NULL;

   const Type *t2 = phase->type( in(2) );

   if( t2 == TypeD::ONE )         // Identity?

     return NULL;                // Skip it

   const TypeD *td = t2->isa_double_constant();

   if( !td ) return NULL;

   if( td->base() != Type::DoubleCon ) return NULL;

   // Check for out of range values

   if( td->is_nan() || !td->is_finite() ) return NULL;

   // Get the value

   double d = td->getd();

   int exp;

   // Only for special case of dividing by a power of 2

   if( frexp(d, &exp) != 0.5 ) return NULL;

   // Limit the range of acceptable exponents

   if( exp < -1021 || exp > 1022 ) return NULL;

   // Compute the reciprocal

   double reciprocal = 1.0 / d;

   assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );

   // return multiplication by the reciprocal

   return (new (phase->C, 3) MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));

 }

 //=============================================================================

 //------------------------------Idealize---------------------------------------

 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {

   // Check for dead control input

   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;

   // Don't bother trying to transform a dead node

   if( in(0) && in(0)->is_top() )  return NULL;

   // Get the modulus

   const Type *t = phase->type( in(2) );

   if( t == Type::TOP ) return NULL;

   const TypeInt *ti = t->is_int();

   // Check for useless control input

   // Check for excluding mod-zero case

   if( in(0) && (ti->_hi < 0 || ti->_lo > 0) ) {

     set_req(0, NULL);        // Yank control input

     return this;

   }

   // See if we are MOD'ing by 2^k or 2^k-1.

   if( !ti->is_con() ) return NULL;

   jint con = ti->get_con();

   Node *hook = new (phase->C, 1) Node(1);

   // First, special check for modulo 2^k-1

   if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {

     uint k = exact_log2(con+1);  // Extract k

     // Basic algorithm by David Detlefs.  See fastmod_int.java for gory details.

     static int unroll_factor[] = { 999, 999, 29, 14, 9, 7, 5, 4, 4, 3, 3, 2, 2, 2, 2, 2, 1 /*past here we assume 1 forever*/};

     int trip_count = 1;

     if( k < ARRAY_SIZE(unroll_factor))  trip_count = unroll_factor[k];

     // If the unroll factor is not too large, and if conditional moves are

     // ok, then use this case

     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {

       Node *x = in(1);            // Value being mod'd

       Node *divisor = in(2);      // Also is mask

       hook->init_req(0, x);       // Add a use to x to prevent him from dying

       // Generate code to reduce X rapidly to nearly 2^k-1.

       for( int i = 0; i < trip_count; i++ ) {

         Node *xl = phase->transform( new (phase->C, 3) AndINode(x,divisor) );

         Node *xh = phase->transform( new (phase->C, 3) RShiftINode(x,phase->intcon(k)) ); // Must be signed

         x = phase->transform( new (phase->C, 3) AddINode(xh,xl) );

         hook->set_req(0, x);

       }

       // Generate sign-fixup code.  Was original value positive?

       // int hack_res = (i >= 0) ? divisor : 1;

       Node *cmp1 = phase->transform( new (phase->C, 3) CmpINode( in(1), phase->intcon(0) ) );

       Node *bol1 = phase->transform( new (phase->C, 2) BoolNode( cmp1, BoolTest::ge ) );

       Node *cmov1= phase->transform( new (phase->C, 4) CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );

       // if( x >= hack_res ) x -= divisor;

       Node *sub  = phase->transform( new (phase->C, 3) SubINode( x, divisor ) );

       Node *cmp2 = phase->transform( new (phase->C, 3) CmpINode( x, cmov1 ) );

       Node *bol2 = phase->transform( new (phase->C, 2) BoolNode( cmp2, BoolTest::ge ) );

       // Convention is to not transform the return value of an Ideal

       // since Ideal is expected to return a modified 'this' or a new node.

       Node *cmov2= new (phase->C, 4) CMoveINode(bol2, x, sub, TypeInt::INT);

       // cmov2 is now the mod

       // Now remove the bogus extra edges used to keep things alive

       if (can_reshape) {

         phase->is_IterGVN()->remove_dead_node(hook);

       } else {

         hook->set_req(0, NULL);   // Just yank bogus edge during Parse phase

       }

       return cmov2;

     }

   }

   // Fell thru, the unroll case is not appropriate. Transform the modulo

   // into a long multiply/int multiply/subtract case

   // Cannot handle mod 0, and min_jint isn't handled by the transform

   if( con == 0 || con == min_jint ) return NULL;

   // Get the absolute value of the constant; at this point, we can use this

   jint pos_con = (con >= 0) ? con : -con;

   // integer Mod 1 is always 0

   if( pos_con == 1 ) return new (phase->C, 1) ConINode(TypeInt::ZERO);

   int log2_con = -1;

   // If this is a power of two, they maybe we can mask it

   if( is_power_of_2(pos_con) ) {

     log2_con = log2_intptr((intptr_t)pos_con);

     const Type *dt = phase->type(in(1));

     const TypeInt *dti = dt->isa_int();

     // See if this can be masked, if the dividend is non-negative

     if( dti && dti->_lo >= 0 )

       return ( new (phase->C, 3) AndINode( in(1), phase->intcon( pos_con-1 ) ) );

   }

   // Save in(1) so that it cannot be changed or deleted

   hook->init_req(0, in(1));

   // Divide using the transform from DivI to MulL

   Node *result = transform_int_divide( phase, in(1), pos_con );

   if (result != NULL) {

     Node *divide = phase->transform(result);

     // Re-multiply, using a shift if this is a power of two

     Node *mult = NULL;

     if( log2_con >= 0 )

       mult = phase->transform( new (phase->C, 3) LShiftINode( divide, phase->intcon( log2_con ) ) );

     else

       mult = phase->transform( new (phase->C, 3) MulINode( divide, phase->intcon( pos_con ) ) );

     // Finally, subtract the multiplied divided value from the original

     result = new (phase->C, 3) SubINode( in(1), mult );

   }

   // Now remove the bogus extra edges used to keep things alive

   if (can_reshape) {

     phase->is_IterGVN()->remove_dead_node(hook);

   } else {

     hook->set_req(0, NULL);       // Just yank bogus edge during Parse phase

   }

   // return the value

   return result;

 }

 //------------------------------Value------------------------------------------

 const Type *ModINode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // We always generate the dynamic check for 0.

   // 0 MOD X is 0

   if( t1 == TypeInt::ZERO ) return TypeInt::ZERO;

   // X MOD X is 0

   if( phase->eqv( in(1), in(2) ) ) return TypeInt::ZERO;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   const TypeInt *i1 = t1->is_int();

   const TypeInt *i2 = t2->is_int();

   if( !i1->is_con() || !i2->is_con() ) {

     if( i1->_lo >= 0 && i2->_lo >= 0 )

       return TypeInt::POS;

     // If both numbers are not constants, we know little.

     return TypeInt::INT;

   }

   // Mod by zero?  Throw exception at runtime!

   if( !i2->get_con() ) return TypeInt::POS;

   // We must be modulo'ing 2 float constants.

   // Check for min_jint % '-1', result is defined to be '0'.

   if( i1->get_con() == min_jint && i2->get_con() == -1 )

     return TypeInt::ZERO;

   return TypeInt::make( i1->get_con() % i2->get_con() );

 }

 //=============================================================================

 //------------------------------Idealize---------------------------------------

 Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {

   // Check for dead control input

   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;

   // Don't bother trying to transform a dead node

   if( in(0) && in(0)->is_top() )  return NULL;

   // Get the modulus

   const Type *t = phase->type( in(2) );

   if( t == Type::TOP ) return NULL;

   const TypeLong *tl = t->is_long();

   // Check for useless control input

   // Check for excluding mod-zero case

   if( in(0) && (tl->_hi < 0 || tl->_lo > 0) ) {

     set_req(0, NULL);        // Yank control input

     return this;

   }

   // See if we are MOD'ing by 2^k or 2^k-1.

   if( !tl->is_con() ) return NULL;

   jlong con = tl->get_con();

   Node *hook = new (phase->C, 1) Node(1);

   // Expand mod

   if( con >= 0 && con < max_jlong && is_power_of_2_long(con+1) ) {

     uint k = exact_log2_long(con+1);  // Extract k

     // Basic algorithm by David Detlefs.  See fastmod_long.java for gory details.

     // Used to help a popular random number generator which does a long-mod

     // of 2^31-1 and shows up in SpecJBB and SciMark.

     static int unroll_factor[] = { 999, 999, 61, 30, 20, 15, 12, 10, 8, 7, 6, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 /*past here we assume 1 forever*/};

     int trip_count = 1;

     if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];

     // If the unroll factor is not too large, and if conditional moves are

     // ok, then use this case

     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {

       Node *x = in(1);            // Value being mod'd

       Node *divisor = in(2);      // Also is mask

       hook->init_req(0, x);       // Add a use to x to prevent him from dying

       // Generate code to reduce X rapidly to nearly 2^k-1.

       for( int i = 0; i < trip_count; i++ ) {

         Node *xl = phase->transform( new (phase->C, 3) AndLNode(x,divisor) );

         Node *xh = phase->transform( new (phase->C, 3) RShiftLNode(x,phase->intcon(k)) ); // Must be signed

         x = phase->transform( new (phase->C, 3) AddLNode(xh,xl) );

         hook->set_req(0, x);    // Add a use to x to prevent him from dying

       }

       // Generate sign-fixup code.  Was original value positive?

       // long hack_res = (i >= 0) ? divisor : CONST64(1);

       Node *cmp1 = phase->transform( new (phase->C, 3) CmpLNode( in(1), phase->longcon(0) ) );

       Node *bol1 = phase->transform( new (phase->C, 2) BoolNode( cmp1, BoolTest::ge ) );

       Node *cmov1= phase->transform( new (phase->C, 4) CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );

       // if( x >= hack_res ) x -= divisor;

       Node *sub  = phase->transform( new (phase->C, 3) SubLNode( x, divisor ) );

       Node *cmp2 = phase->transform( new (phase->C, 3) CmpLNode( x, cmov1 ) );

       Node *bol2 = phase->transform( new (phase->C, 2) BoolNode( cmp2, BoolTest::ge ) );

       // Convention is to not transform the return value of an Ideal

       // since Ideal is expected to return a modified 'this' or a new node.

       Node *cmov2= new (phase->C, 4) CMoveLNode(bol2, x, sub, TypeLong::LONG);

       // cmov2 is now the mod

       // Now remove the bogus extra edges used to keep things alive

       if (can_reshape) {

         phase->is_IterGVN()->remove_dead_node(hook);

       } else {

         hook->set_req(0, NULL);   // Just yank bogus edge during Parse phase

       }

       return cmov2;

     }

   }

   // Fell thru, the unroll case is not appropriate. Transform the modulo

   // into a long multiply/int multiply/subtract case

   // Cannot handle mod 0, and min_jlong isn't handled by the transform

   if( con == 0 || con == min_jlong ) return NULL;

   // Get the absolute value of the constant; at this point, we can use this

   jlong pos_con = (con >= 0) ? con : -con;

   // integer Mod 1 is always 0

   if( pos_con == 1 ) return new (phase->C, 1) ConLNode(TypeLong::ZERO);

   int log2_con = -1;

   // If this is a power of two, then maybe we can mask it

   if( is_power_of_2_long(pos_con) ) {

     log2_con = exact_log2_long(pos_con);

     const Type *dt = phase->type(in(1));

     const TypeLong *dtl = dt->isa_long();

     // See if this can be masked, if the dividend is non-negative

     if( dtl && dtl->_lo >= 0 )

       return ( new (phase->C, 3) AndLNode( in(1), phase->longcon( pos_con-1 ) ) );

   }

   // Save in(1) so that it cannot be changed or deleted

   hook->init_req(0, in(1));

   // Divide using the transform from DivL to MulL

   Node *result = transform_long_divide( phase, in(1), pos_con );

   if (result != NULL) {

     Node *divide = phase->transform(result);

     // Re-multiply, using a shift if this is a power of two

     Node *mult = NULL;

     if( log2_con >= 0 )

       mult = phase->transform( new (phase->C, 3) LShiftLNode( divide, phase->intcon( log2_con ) ) );

     else

       mult = phase->transform( new (phase->C, 3) MulLNode( divide, phase->longcon( pos_con ) ) );

     // Finally, subtract the multiplied divided value from the original

     result = new (phase->C, 3) SubLNode( in(1), mult );

   }

   // Now remove the bogus extra edges used to keep things alive

   if (can_reshape) {

     phase->is_IterGVN()->remove_dead_node(hook);

   } else {

     hook->set_req(0, NULL);       // Just yank bogus edge during Parse phase

   }

   // return the value

   return result;

 }

 //------------------------------Value------------------------------------------

 const Type *ModLNode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // We always generate the dynamic check for 0.

   // 0 MOD X is 0

   if( t1 == TypeLong::ZERO ) return TypeLong::ZERO;

   // X MOD X is 0

   if( phase->eqv( in(1), in(2) ) ) return TypeLong::ZERO;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   const TypeLong *i1 = t1->is_long();

   const TypeLong *i2 = t2->is_long();

   if( !i1->is_con() || !i2->is_con() ) {

     if( i1->_lo >= CONST64(0) && i2->_lo >= CONST64(0) )

       return TypeLong::POS;

     // If both numbers are not constants, we know little.

     return TypeLong::LONG;

   }

   // Mod by zero?  Throw exception at runtime!

   if( !i2->get_con() ) return TypeLong::POS;

   // We must be modulo'ing 2 float constants.

   // Check for min_jint % '-1', result is defined to be '0'.

   if( i1->get_con() == min_jlong && i2->get_con() == -1 )

     return TypeLong::ZERO;

   return TypeLong::make( i1->get_con() % i2->get_con() );

 }

 //=============================================================================

 //------------------------------Value------------------------------------------

 const Type *ModFNode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   // If either number is not a constant, we know nothing.

   if ((t1->base() != Type::FloatCon) || (t2->base() != Type::FloatCon)) {

     return Type::FLOAT;         // note: x%x can be either NaN or 0

   }

   float f1 = t1->getf();

   float f2 = t2->getf();

   jint  x1 = jint_cast(f1);     // note:  *(int*)&f1, not just (int)f1

   jint  x2 = jint_cast(f2);

   // If either is a NaN, return an input NaN

   if (g_isnan(f1))    return t1;

   if (g_isnan(f2))    return t2;

   // If an operand is infinity or the divisor is +/- zero, punt.

   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jint)

     return Type::FLOAT;

   // We must be modulo'ing 2 float constants.

   // Make sure that the sign of the fmod is equal to the sign of the dividend

   jint xr = jint_cast(fmod(f1, f2));

   if ((x1 ^ xr) < 0) {

     xr ^= min_jint;

   }

   return TypeF::make(jfloat_cast(xr));

 }

 //=============================================================================

 //------------------------------Value------------------------------------------

 const Type *ModDNode::Value( PhaseTransform *phase ) const {

   // Either input is TOP ==> the result is TOP

   const Type *t1 = phase->type( in(1) );

   const Type *t2 = phase->type( in(2) );

   if( t1 == Type::TOP ) return Type::TOP;

   if( t2 == Type::TOP ) return Type::TOP;

   // Either input is BOTTOM ==> the result is the local BOTTOM

   const Type *bot = bottom_type();

   if( (t1 == bot) || (t2 == bot) ||

       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )

     return bot;

   // If either number is not a constant, we know nothing.

   if ((t1->base() != Type::DoubleCon) || (t2->base() != Type::DoubleCon)) {

     return Type::DOUBLE;        // note: x%x can be either NaN or 0

   }

   double f1 = t1->getd();

   double f2 = t2->getd();

   jlong  x1 = jlong_cast(f1);   // note:  *(long*)&f1, not just (long)f1

   jlong  x2 = jlong_cast(f2);

   // If either is a NaN, return an input NaN

   if (g_isnan(f1))    return t1;

   if (g_isnan(f2))    return t2;

   // If an operand is infinity or the divisor is +/- zero, punt.

   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jlong)

     return Type::DOUBLE;

   // We must be modulo'ing 2 double constants.

   // Make sure that the sign of the fmod is equal to the sign of the dividend

   jlong xr = jlong_cast(fmod(f1, f2));

   if ((x1 ^ xr) < 0) {

     xr ^= min_jlong;

   }

   return TypeD::make(jdouble_cast(xr));

 }

 //=============================================================================

 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {

   init_req(0, c);

   init_req(1, dividend);

   init_req(2, divisor);

 }

 //------------------------------make------------------------------------------

 DivModINode* DivModINode::make(Compile* C, Node* div_or_mod) {

   Node* n = div_or_mod;

   assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,

          "only div or mod input pattern accepted");

   DivModINode* divmod = new (C, 3) DivModINode(n->in(0), n->in(1), n->in(2));

   Node*        dproj  = new (C, 1) ProjNode(divmod, DivModNode::div_proj_num);

   Node*        mproj  = new (C, 1) ProjNode(divmod, DivModNode::mod_proj_num);

   return divmod;

 }

 //------------------------------make------------------------------------------

 DivModLNode* DivModLNode::make(Compile* C, Node* div_or_mod) {

   Node* n = div_or_mod;

   assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,

          "only div or mod input pattern accepted");

   DivModLNode* divmod = new (C, 3) DivModLNode(n->in(0), n->in(1), n->in(2));

   Node*        dproj  = new (C, 1) ProjNode(divmod, DivModNode::div_proj_num);

   Node*        mproj  = new (C, 1) ProjNode(divmod, DivModNode::mod_proj_num);

   return divmod;

 }

 //------------------------------match------------------------------------------

 // return result(s) along with their RegMask info

 Node *DivModINode::match( const ProjNode *proj, const Matcher *match ) {

   uint ideal_reg = proj->ideal_reg();

   RegMask rm;

   if (proj->_con == div_proj_num) {

     rm = match->divI_proj_mask();

   } else {

     assert(proj->_con == mod_proj_num, "must be div or mod projection");

     rm = match->modI_proj_mask();

   }

   return new (match->C, 1)MachProjNode(this, proj->_con, rm, ideal_reg);

 }

 //------------------------------match------------------------------------------

 // return result(s) along with their RegMask info

 Node *DivModLNode::match( const ProjNode *proj, const Matcher *match ) {

   uint ideal_reg = proj->ideal_reg();

   RegMask rm;

   if (proj->_con == div_proj_num) {

     rm = match->divL_proj_mask();

   } else {

     assert(proj->_con == mod_proj_num, "must be div or mod projection");

     rm = match->modL_proj_mask();

   }

   return new (match->C, 1)MachProjNode(this, proj->_con, rm, ideal_reg);

 }