divnode.cpp

/*
 * Copyright (c) 1997, 2025, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * 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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#include "memory/allocation.inline.hpp"
#include "opto/addnode.hpp"
#include "opto/connode.hpp"
#include "opto/convertnode.hpp"
#include "opto/divnode.hpp"
#include "opto/machnode.hpp"
#include "opto/movenode.hpp"
#include "opto/matcher.hpp"
#include "opto/mulnode.hpp"
#include "opto/phaseX.hpp"
#include "opto/subnode.hpp"
#include "utilities/powerOfTwo.hpp"
#include "opto/runtime.hpp"

// Portions of code courtesy of Clifford Click

// Optimization - Graph Style

#include <math.h>

ModFloatingNode::ModFloatingNode(Compile* C, const TypeFunc* tf, const char* name) : CallLeafNode(tf, nullptr, name, TypeRawPtr::BOTTOM) {
  add_flag(Flag_is_macro);
  C->add_macro_node(this);
}

ModDNode::ModDNode(Compile* C, Node* a, Node* b) : ModFloatingNode(C, OptoRuntime::Math_DD_D_Type(), "drem") {
  init_req(TypeFunc::Parms + 0, a);
  init_req(TypeFunc::Parms + 1, C->top());
  init_req(TypeFunc::Parms + 2, b);
  init_req(TypeFunc::Parms + 3, C->top());
}

ModFNode::ModFNode(Compile* C, Node* a, Node* b) : ModFloatingNode(C, OptoRuntime::modf_Type(), "frem") {
  init_req(TypeFunc::Parms + 0, a);
  init_req(TypeFunc::Parms + 1, b);
}

//----------------------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 = nullptr;

  if (d == 1) {
    // division by +/- 1
    if (!d_pos) {
      // Just negate the value
      q = new 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 = log2i_graceful(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 RShiftINode(dividend, phase->intcon(N - 1)));
      // Mask sign bit to the low sign bits
      Node *round = phase->transform(new URShiftINode(sign, phase->intcon(N - l)));
      // Round up before shifting
      dividend = phase->transform(new AddINode(dividend, round));
    }

    // Shift for division
    q = new RShiftINode(dividend, phase->intcon(l));

    if (!d_pos) {
      q = new 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 ConvI2LNode(dividend));

      // Compute the high half of the dividend x magic multiplication
      Node *mul_hi = phase->transform(new MulLNode(dividend_long, magic));

      if (magic_const < 0) {
        mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N)));
        mul_hi = phase->transform(new 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 AddINode(dividend, mul_hi));

        // Shift over the (adjusted) mulhi
        if (shift_const != 0) {
          mul_hi = phase->transform(new RShiftINode(mul_hi, phase->intcon(shift_const)));
        }
      } else {
        // No add is required, we can merge the shifts together.
        mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N + shift_const)));
        mul_hi = phase->transform(new ConvL2INode(mul_hi));
      }

      // Get a 0 or -1 from the sign of the dividend.
      Node *addend0 = mul_hi;
      Node *addend1 = phase->transform(new 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 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 = UCONST64(0x8000000000000000);     // 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 MulHiLNode(dividend, v);
  }

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

  // Dummy node to keep intermediate nodes alive during construction
  Node* hook = new Node(4);

  // u0 = u & 0xFFFFFFFF;  u1 = u >> 32;
  Node* u0 = phase->transform(new AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
  Node* u1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N / 2)));
  hook->init_req(0, u0);
  hook->init_req(1, u1);

  // 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 MulLNode(u0, v0));

  // t = u1*v0 + (w0 >> 32);
  Node* u1v0 = phase->transform(new MulLNode(u1, v0));
  Node* temp = phase->transform(new URShiftLNode(w0, phase->intcon(N / 2)));
  Node* t    = phase->transform(new AddLNode(u1v0, temp));
  hook->init_req(2, t);

  // w1 = t & 0xFFFFFFFF;
  Node* w1 = phase->transform(new AndLNode(t, phase->longcon(0xFFFFFFFF)));
  hook->init_req(3, w1);

  // w2 = t >> 32;
  Node* w2 = phase->transform(new RShiftLNode(t, phase->intcon(N / 2)));

  // w1 = u0*v1 + w1;
  Node* u0v1 = phase->transform(new MulLNode(u0, v1));
  w1         = phase->transform(new AddLNode(u0v1, w1));

  // return u1*v1 + w2 + (w1 >> 32);
  Node* u1v1  = phase->transform(new MulLNode(u1, v1));
  Node* temp1 = phase->transform(new AddLNode(u1v1, w2));
  Node* temp2 = phase->transform(new RShiftLNode(w1, phase->intcon(N / 2)));

  // Remove the bogus extra edges used to keep things alive
  hook->destruct(phase);

  return new 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 = nullptr;

  if (d == 1) {
    // division by +/- 1
    if (!d_pos) {
      // Just negate the value
      q = new SubLNode(phase->longcon(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 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(-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 = log2i_graceful(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 RShiftLNode(dividend, phase->intcon(N - 1)));
      // Mask sign bit to the low sign bits
      Node *round = phase->transform(new URShiftLNode(sign, phase->intcon(N - l)));
      // Round up before shifting
      dividend = phase->transform(new AddLNode(dividend, round));
    }

    // Shift for division
    q = new RShiftLNode(dividend, phase->intcon(l));

    if (!d_pos) {
      q = new 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 AddLNode(dividend, mul_hi));
      }

      // Shift over the (adjusted) mulhi
      if (shift_const != 0) {
        mul_hi = phase->transform(new 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 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 SubLNode(addend0, addend1);
    }
  }

  return q;
}

template <typename TypeClass, typename Unsigned>
Node* unsigned_div_ideal(PhaseGVN* phase, bool can_reshape, Node* div) {
  // Check for dead control input
  if (div->in(0) != nullptr && div->remove_dead_region(phase, can_reshape)) {
    return div;
  }
  // Don't bother trying to transform a dead node
  if (div->in(0) != nullptr && div->in(0)->is_top()) {
    return nullptr;
  }

  const Type* t = phase->type(div->in(2));
  if (t == Type::TOP) {
    return nullptr;
  }
  const TypeClass* type_divisor = t->cast<TypeClass>();

  // Check for useless control input
  // Check for excluding div-zero case
  if (div->in(0) != nullptr && (type_divisor->_hi < 0 || type_divisor->_lo > 0)) {
    div->set_req(0, nullptr); // Yank control input
    return div;
  }

  if (!type_divisor->is_con()) {
    return nullptr;
  }
  Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con()); // Get divisor

  if (divisor == 0 || divisor == 1) {
    return nullptr; // Dividing by zero constant does not idealize
  }

  if (is_power_of_2(divisor)) {
    return make_urshift<TypeClass>(div->in(1), phase->intcon(log2i_graceful(divisor)));
  }

  return nullptr;
}


//=============================================================================
//------------------------------Identity---------------------------------------
// If the divisor is 1, we are an identity on the dividend.
Node* DivINode::Identity(PhaseGVN* 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 nullptr;

  const Type *t = phase->type( in(2) );
  if( t == TypeInt::ONE )      // Identity?
    return nullptr;            // Skip it

  const TypeInt *ti = t->isa_int();
  if( !ti ) return nullptr;

  // Check for useless control input
  // Check for excluding div-zero case
  if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
    set_req(0, nullptr);           // Yank control input
    return this;
  }

  if( !ti->is_con() ) return nullptr;
  jint i = ti->get_con();       // Get divisor

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

  // Dividing by MININT does not optimize as a power-of-2 shift.
  if( i == min_jint ) return nullptr;

  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(PhaseGVN* 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 (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_t 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_t 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(PhaseGVN* 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 nullptr;

  const Type *t = phase->type( in(2) );
  if( t == TypeLong::ONE )      // Identity?
    return nullptr;             // Skip it

  const TypeLong *tl = t->isa_long();
  if( !tl ) return nullptr;

  // Check for useless control input
  // Check for excluding div-zero case
  if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
    set_req(0, nullptr);         // Yank control input
    return this;
  }

  if( !tl->is_con() ) return nullptr;
  jlong l = tl->get_con();      // Get divisor

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

  // Dividing by MINLONG does not optimize as a power-of-2 shift.
  if( l == min_jlong ) return nullptr;

  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(PhaseGVN* 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 (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(PhaseGVN* 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 (in(1) == in(2) && t1->base() == Type::FloatCon &&
      !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(PhaseGVN* 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 nullptr;

  const Type *t2 = phase->type( in(2) );
  if( t2 == TypeF::ONE )         // Identity?
    return nullptr;              // Skip it

  const TypeF *tf = t2->isa_float_constant();
  if( !tf ) return nullptr;
  if( tf->base() != Type::FloatCon ) return nullptr;

  // Check for out of range values
  if( tf->is_nan() || !tf->is_finite() ) return nullptr;

  // 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 nullptr;

  // Limit the range of acceptable exponents
  if( exp < -126 || exp > 126 ) return nullptr;

  // 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 MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
}
//=============================================================================
//------------------------------Value------------------------------------------
// An DivHFNode divides its inputs.  The third input is a Control input, used to
// prevent hoisting the divide above an unsafe test.
const Type* DivHFNode::Value(PhaseGVN* 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 (in(1) == in(2) && t1->base() == Type::HalfFloatCon &&
      !g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) { // could be negative ZERO or NaN
    return TypeH::ONE;
  }

  if (t2 == TypeH::ONE) {
    return t1;
  }

  // If divisor is a constant and not zero, divide the numbers
  if (t1->base() == Type::HalfFloatCon &&
      t2->base() == Type::HalfFloatCon &&
      t2->getf() != 0.0)  {
    // could be negative zero
    return TypeH::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 TypeHF::ZERO is not sufficient as it could be negative zero

  if (t1 == TypeH::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0) {
    return TypeH::ZERO;
  }

  // If divisor or dividend is nan then result is nan.
  if (g_isnan(t1->getf()) || g_isnan(t2->getf())) {
    return TypeH::make(NAN);
  }

  // Otherwise we give up all hope
  return Type::HALF_FLOAT;
}

//-----------------------------------------------------------------------------
// Dividing by self is 1.
// IF the divisor is 1, we are an identity on the dividend.
Node* DivHFNode::Identity(PhaseGVN* phase) {
  return (phase->type( in(2) ) == TypeH::ONE) ? in(1) : this;
}


//------------------------------Idealize---------------------------------------
Node* DivHFNode::Ideal(PhaseGVN* phase, bool can_reshape) {
  if (in(0) != nullptr && remove_dead_region(phase, can_reshape))  return this;
  // Don't bother trying to transform a dead node
  if (in(0) != nullptr && in(0)->is_top())  { return nullptr; }

  const Type* t2 = phase->type(in(2));
  if (t2 == TypeH::ONE) {      // Identity?
    return nullptr;            // Skip it
  }
  const TypeH* tf = t2->isa_half_float_constant();
  if(tf == nullptr) { return nullptr; }
  if(tf->base() != Type::HalfFloatCon) { return nullptr; }

  // Check for out of range values
  if(tf->is_nan() || !tf->is_finite()) { return nullptr; }

  // Get the value
  float f = tf->getf();
  int exp;

  // Consider the following geometric progression series of POT(power of two) numbers.
  // 0.5 x 2^0 = 0.5, 0.5 x 2^1 = 1.0, 0.5 x 2^2 = 2.0, 0.5 x 2^3 = 4.0 ... 0.5 x 2^n,
  // In all the above cases, normalized mantissa returned by frexp routine will
  // be exactly equal to 0.5 while exponent will be 0,1,2,3...n
  // Perform division to multiplication transform only if divisor is a POT value.
  if(frexp((double)f, &exp) != 0.5) { return nullptr; }

  // Limit the range of acceptable exponents
  if(exp < -14 || exp > 15) { return nullptr; }

  // Since divisor is a POT number, hence its reciprocal will never
  // overflow 11 bits precision range of Float16
  // value if exponent returned by frexp routine strictly lie
  // within the exponent range of normal min(0x1.0P-14) and
  // normal max(0x1.ffcP+15) values.
  // Thus we can safely compute the reciprocal of divisor without
  // any concerns about the precision loss and transform the division
  // into a multiplication operation.
  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 MulHFNode(in(1), phase->makecon(TypeH::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(PhaseGVN* 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 (in(1) == in(2) && t1->base() == Type::DoubleCon &&
      !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;

  // IA32 would only execute this for non-strict FP, which is never the
  // case now.
#if ! defined(IA32)
  // 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() );
#endif

  // 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(PhaseGVN* 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 nullptr;

  const Type *t2 = phase->type( in(2) );
  if( t2 == TypeD::ONE )         // Identity?
    return nullptr;              // Skip it

  const TypeD *td = t2->isa_double_constant();
  if( !td ) return nullptr;
  if( td->base() != Type::DoubleCon ) return nullptr;

  // Check for out of range values
  if( td->is_nan() || !td->is_finite() ) return nullptr;

  // 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 nullptr;

  // Limit the range of acceptable exponents
  if( exp < -1021 || exp > 1022 ) return nullptr;