src/share/vm/opto/divnode.cpp

changeset 0
f90c822e73f8
child 6876
710a3c8b516e
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/share/vm/opto/divnode.cpp	Wed Apr 27 01:25:04 2016 +0800
     1.3 @@ -0,0 +1,1325 @@
     1.4 +/*
     1.5 + * Copyright (c) 1997, 2012, Oracle and/or its affiliates. All rights reserved.
     1.6 + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
     1.7 + *
     1.8 + * This code is free software; you can redistribute it and/or modify it
     1.9 + * under the terms of the GNU General Public License version 2 only, as
    1.10 + * published by the Free Software Foundation.
    1.11 + *
    1.12 + * This code is distributed in the hope that it will be useful, but WITHOUT
    1.13 + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    1.14 + * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    1.15 + * version 2 for more details (a copy is included in the LICENSE file that
    1.16 + * accompanied this code).
    1.17 + *
    1.18 + * You should have received a copy of the GNU General Public License version
    1.19 + * 2 along with this work; if not, write to the Free Software Foundation,
    1.20 + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
    1.21 + *
    1.22 + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
    1.23 + * or visit www.oracle.com if you need additional information or have any
    1.24 + * questions.
    1.25 + *
    1.26 + */
    1.27 +
    1.28 +#include "precompiled.hpp"
    1.29 +#include "memory/allocation.inline.hpp"
    1.30 +#include "opto/addnode.hpp"
    1.31 +#include "opto/connode.hpp"
    1.32 +#include "opto/divnode.hpp"
    1.33 +#include "opto/machnode.hpp"
    1.34 +#include "opto/matcher.hpp"
    1.35 +#include "opto/mulnode.hpp"
    1.36 +#include "opto/phaseX.hpp"
    1.37 +#include "opto/subnode.hpp"
    1.38 +
    1.39 +// Portions of code courtesy of Clifford Click
    1.40 +
    1.41 +// Optimization - Graph Style
    1.42 +
    1.43 +#include <math.h>
    1.44 +
    1.45 +//----------------------magic_int_divide_constants-----------------------------
    1.46 +// Compute magic multiplier and shift constant for converting a 32 bit divide
    1.47 +// by constant into a multiply/shift/add series. Return false if calculations
    1.48 +// fail.
    1.49 +//
    1.50 +// Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
    1.51 +// minor type name and parameter changes.
    1.52 +static bool magic_int_divide_constants(jint d, jint &M, jint &s) {
    1.53 +  int32_t p;
    1.54 +  uint32_t ad, anc, delta, q1, r1, q2, r2, t;
    1.55 +  const uint32_t two31 = 0x80000000L;     // 2**31.
    1.56 +
    1.57 +  ad = ABS(d);
    1.58 +  if (d == 0 || d == 1) return false;
    1.59 +  t = two31 + ((uint32_t)d >> 31);
    1.60 +  anc = t - 1 - t%ad;     // Absolute value of nc.
    1.61 +  p = 31;                 // Init. p.
    1.62 +  q1 = two31/anc;         // Init. q1 = 2**p/|nc|.
    1.63 +  r1 = two31 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
    1.64 +  q2 = two31/ad;          // Init. q2 = 2**p/|d|.
    1.65 +  r2 = two31 - q2*ad;     // Init. r2 = rem(2**p, |d|).
    1.66 +  do {
    1.67 +    p = p + 1;
    1.68 +    q1 = 2*q1;            // Update q1 = 2**p/|nc|.
    1.69 +    r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
    1.70 +    if (r1 >= anc) {      // (Must be an unsigned
    1.71 +      q1 = q1 + 1;        // comparison here).
    1.72 +      r1 = r1 - anc;
    1.73 +    }
    1.74 +    q2 = 2*q2;            // Update q2 = 2**p/|d|.
    1.75 +    r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
    1.76 +    if (r2 >= ad) {       // (Must be an unsigned
    1.77 +      q2 = q2 + 1;        // comparison here).
    1.78 +      r2 = r2 - ad;
    1.79 +    }
    1.80 +    delta = ad - r2;
    1.81 +  } while (q1 < delta || (q1 == delta && r1 == 0));
    1.82 +
    1.83 +  M = q2 + 1;
    1.84 +  if (d < 0) M = -M;      // Magic number and
    1.85 +  s = p - 32;             // shift amount to return.
    1.86 +
    1.87 +  return true;
    1.88 +}
    1.89 +
    1.90 +//--------------------------transform_int_divide-------------------------------
    1.91 +// Convert a division by constant divisor into an alternate Ideal graph.
    1.92 +// Return NULL if no transformation occurs.
    1.93 +static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) {
    1.94 +
    1.95 +  // Check for invalid divisors
    1.96 +  assert( divisor != 0 && divisor != min_jint,
    1.97 +          "bad divisor for transforming to long multiply" );
    1.98 +
    1.99 +  bool d_pos = divisor >= 0;
   1.100 +  jint d = d_pos ? divisor : -divisor;
   1.101 +  const int N = 32;
   1.102 +
   1.103 +  // Result
   1.104 +  Node *q = NULL;
   1.105 +
   1.106 +  if (d == 1) {
   1.107 +    // division by +/- 1
   1.108 +    if (!d_pos) {
   1.109 +      // Just negate the value
   1.110 +      q = new (phase->C) SubINode(phase->intcon(0), dividend);
   1.111 +    }
   1.112 +  } else if ( is_power_of_2(d) ) {
   1.113 +    // division by +/- a power of 2
   1.114 +
   1.115 +    // See if we can simply do a shift without rounding
   1.116 +    bool needs_rounding = true;
   1.117 +    const Type *dt = phase->type(dividend);
   1.118 +    const TypeInt *dti = dt->isa_int();
   1.119 +    if (dti && dti->_lo >= 0) {
   1.120 +      // we don't need to round a positive dividend
   1.121 +      needs_rounding = false;
   1.122 +    } else if( dividend->Opcode() == Op_AndI ) {
   1.123 +      // An AND mask of sufficient size clears the low bits and
   1.124 +      // I can avoid rounding.
   1.125 +      const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int();
   1.126 +      if( andconi_t && andconi_t->is_con() ) {
   1.127 +        jint andconi = andconi_t->get_con();
   1.128 +        if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) {
   1.129 +          if( (-andconi) == d ) // Remove AND if it clears bits which will be shifted
   1.130 +            dividend = dividend->in(1);
   1.131 +          needs_rounding = false;
   1.132 +        }
   1.133 +      }
   1.134 +    }
   1.135 +
   1.136 +    // Add rounding to the shift to handle the sign bit
   1.137 +    int l = log2_intptr(d-1)+1;
   1.138 +    if (needs_rounding) {
   1.139 +      // Divide-by-power-of-2 can be made into a shift, but you have to do
   1.140 +      // more math for the rounding.  You need to add 0 for positive
   1.141 +      // numbers, and "i-1" for negative numbers.  Example: i=4, so the
   1.142 +      // shift is by 2.  You need to add 3 to negative dividends and 0 to
   1.143 +      // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
   1.144 +      // (-2+3)>>2 becomes 0, etc.
   1.145 +
   1.146 +      // Compute 0 or -1, based on sign bit
   1.147 +      Node *sign = phase->transform(new (phase->C) RShiftINode(dividend, phase->intcon(N - 1)));
   1.148 +      // Mask sign bit to the low sign bits
   1.149 +      Node *round = phase->transform(new (phase->C) URShiftINode(sign, phase->intcon(N - l)));
   1.150 +      // Round up before shifting
   1.151 +      dividend = phase->transform(new (phase->C) AddINode(dividend, round));
   1.152 +    }
   1.153 +
   1.154 +    // Shift for division
   1.155 +    q = new (phase->C) RShiftINode(dividend, phase->intcon(l));
   1.156 +
   1.157 +    if (!d_pos) {
   1.158 +      q = new (phase->C) SubINode(phase->intcon(0), phase->transform(q));
   1.159 +    }
   1.160 +  } else {
   1.161 +    // Attempt the jint constant divide -> multiply transform found in
   1.162 +    //   "Division by Invariant Integers using Multiplication"
   1.163 +    //     by Granlund and Montgomery
   1.164 +    // See also "Hacker's Delight", chapter 10 by Warren.
   1.165 +
   1.166 +    jint magic_const;
   1.167 +    jint shift_const;
   1.168 +    if (magic_int_divide_constants(d, magic_const, shift_const)) {
   1.169 +      Node *magic = phase->longcon(magic_const);
   1.170 +      Node *dividend_long = phase->transform(new (phase->C) ConvI2LNode(dividend));
   1.171 +
   1.172 +      // Compute the high half of the dividend x magic multiplication
   1.173 +      Node *mul_hi = phase->transform(new (phase->C) MulLNode(dividend_long, magic));
   1.174 +
   1.175 +      if (magic_const < 0) {
   1.176 +        mul_hi = phase->transform(new (phase->C) RShiftLNode(mul_hi, phase->intcon(N)));
   1.177 +        mul_hi = phase->transform(new (phase->C) ConvL2INode(mul_hi));
   1.178 +
   1.179 +        // The magic multiplier is too large for a 32 bit constant. We've adjusted
   1.180 +        // it down by 2^32, but have to add 1 dividend back in after the multiplication.
   1.181 +        // This handles the "overflow" case described by Granlund and Montgomery.
   1.182 +        mul_hi = phase->transform(new (phase->C) AddINode(dividend, mul_hi));
   1.183 +
   1.184 +        // Shift over the (adjusted) mulhi
   1.185 +        if (shift_const != 0) {
   1.186 +          mul_hi = phase->transform(new (phase->C) RShiftINode(mul_hi, phase->intcon(shift_const)));
   1.187 +        }
   1.188 +      } else {
   1.189 +        // No add is required, we can merge the shifts together.
   1.190 +        mul_hi = phase->transform(new (phase->C) RShiftLNode(mul_hi, phase->intcon(N + shift_const)));
   1.191 +        mul_hi = phase->transform(new (phase->C) ConvL2INode(mul_hi));
   1.192 +      }
   1.193 +
   1.194 +      // Get a 0 or -1 from the sign of the dividend.
   1.195 +      Node *addend0 = mul_hi;
   1.196 +      Node *addend1 = phase->transform(new (phase->C) RShiftINode(dividend, phase->intcon(N-1)));
   1.197 +
   1.198 +      // If the divisor is negative, swap the order of the input addends;
   1.199 +      // this has the effect of negating the quotient.
   1.200 +      if (!d_pos) {
   1.201 +        Node *temp = addend0; addend0 = addend1; addend1 = temp;
   1.202 +      }
   1.203 +
   1.204 +      // Adjust the final quotient by subtracting -1 (adding 1)
   1.205 +      // from the mul_hi.
   1.206 +      q = new (phase->C) SubINode(addend0, addend1);
   1.207 +    }
   1.208 +  }
   1.209 +
   1.210 +  return q;
   1.211 +}
   1.212 +
   1.213 +//---------------------magic_long_divide_constants-----------------------------
   1.214 +// Compute magic multiplier and shift constant for converting a 64 bit divide
   1.215 +// by constant into a multiply/shift/add series. Return false if calculations
   1.216 +// fail.
   1.217 +//
   1.218 +// Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
   1.219 +// minor type name and parameter changes.  Adjusted to 64 bit word width.
   1.220 +static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) {
   1.221 +  int64_t p;
   1.222 +  uint64_t ad, anc, delta, q1, r1, q2, r2, t;
   1.223 +  const uint64_t two63 = 0x8000000000000000LL;     // 2**63.
   1.224 +
   1.225 +  ad = ABS(d);
   1.226 +  if (d == 0 || d == 1) return false;
   1.227 +  t = two63 + ((uint64_t)d >> 63);
   1.228 +  anc = t - 1 - t%ad;     // Absolute value of nc.
   1.229 +  p = 63;                 // Init. p.
   1.230 +  q1 = two63/anc;         // Init. q1 = 2**p/|nc|.
   1.231 +  r1 = two63 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
   1.232 +  q2 = two63/ad;          // Init. q2 = 2**p/|d|.
   1.233 +  r2 = two63 - q2*ad;     // Init. r2 = rem(2**p, |d|).
   1.234 +  do {
   1.235 +    p = p + 1;
   1.236 +    q1 = 2*q1;            // Update q1 = 2**p/|nc|.
   1.237 +    r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
   1.238 +    if (r1 >= anc) {      // (Must be an unsigned
   1.239 +      q1 = q1 + 1;        // comparison here).
   1.240 +      r1 = r1 - anc;
   1.241 +    }
   1.242 +    q2 = 2*q2;            // Update q2 = 2**p/|d|.
   1.243 +    r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
   1.244 +    if (r2 >= ad) {       // (Must be an unsigned
   1.245 +      q2 = q2 + 1;        // comparison here).
   1.246 +      r2 = r2 - ad;
   1.247 +    }
   1.248 +    delta = ad - r2;
   1.249 +  } while (q1 < delta || (q1 == delta && r1 == 0));
   1.250 +
   1.251 +  M = q2 + 1;
   1.252 +  if (d < 0) M = -M;      // Magic number and
   1.253 +  s = p - 64;             // shift amount to return.
   1.254 +
   1.255 +  return true;
   1.256 +}
   1.257 +
   1.258 +//---------------------long_by_long_mulhi--------------------------------------
   1.259 +// Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication
   1.260 +static Node* long_by_long_mulhi(PhaseGVN* phase, Node* dividend, jlong magic_const) {
   1.261 +  // If the architecture supports a 64x64 mulhi, there is
   1.262 +  // no need to synthesize it in ideal nodes.
   1.263 +  if (Matcher::has_match_rule(Op_MulHiL)) {
   1.264 +    Node* v = phase->longcon(magic_const);
   1.265 +    return new (phase->C) MulHiLNode(dividend, v);
   1.266 +  }
   1.267 +
   1.268 +  // Taken from Hacker's Delight, Fig. 8-2. Multiply high signed.
   1.269 +  // (http://www.hackersdelight.org/HDcode/mulhs.c)
   1.270 +  //
   1.271 +  // int mulhs(int u, int v) {
   1.272 +  //    unsigned u0, v0, w0;
   1.273 +  //    int u1, v1, w1, w2, t;
   1.274 +  //
   1.275 +  //    u0 = u & 0xFFFF;  u1 = u >> 16;
   1.276 +  //    v0 = v & 0xFFFF;  v1 = v >> 16;
   1.277 +  //    w0 = u0*v0;
   1.278 +  //    t  = u1*v0 + (w0 >> 16);
   1.279 +  //    w1 = t & 0xFFFF;
   1.280 +  //    w2 = t >> 16;
   1.281 +  //    w1 = u0*v1 + w1;
   1.282 +  //    return u1*v1 + w2 + (w1 >> 16);
   1.283 +  // }
   1.284 +  //
   1.285 +  // Note: The version above is for 32x32 multiplications, while the
   1.286 +  // following inline comments are adapted to 64x64.
   1.287 +
   1.288 +  const int N = 64;
   1.289 +
   1.290 +  // Dummy node to keep intermediate nodes alive during construction
   1.291 +  Node* hook = new (phase->C) Node(4);
   1.292 +
   1.293 +  // u0 = u & 0xFFFFFFFF;  u1 = u >> 32;
   1.294 +  Node* u0 = phase->transform(new (phase->C) AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
   1.295 +  Node* u1 = phase->transform(new (phase->C) RShiftLNode(dividend, phase->intcon(N / 2)));
   1.296 +  hook->init_req(0, u0);
   1.297 +  hook->init_req(1, u1);
   1.298 +
   1.299 +  // v0 = v & 0xFFFFFFFF;  v1 = v >> 32;
   1.300 +  Node* v0 = phase->longcon(magic_const & 0xFFFFFFFF);
   1.301 +  Node* v1 = phase->longcon(magic_const >> (N / 2));
   1.302 +
   1.303 +  // w0 = u0*v0;
   1.304 +  Node* w0 = phase->transform(new (phase->C) MulLNode(u0, v0));
   1.305 +
   1.306 +  // t = u1*v0 + (w0 >> 32);
   1.307 +  Node* u1v0 = phase->transform(new (phase->C) MulLNode(u1, v0));
   1.308 +  Node* temp = phase->transform(new (phase->C) URShiftLNode(w0, phase->intcon(N / 2)));
   1.309 +  Node* t    = phase->transform(new (phase->C) AddLNode(u1v0, temp));
   1.310 +  hook->init_req(2, t);
   1.311 +
   1.312 +  // w1 = t & 0xFFFFFFFF;
   1.313 +  Node* w1 = phase->transform(new (phase->C) AndLNode(t, phase->longcon(0xFFFFFFFF)));
   1.314 +  hook->init_req(3, w1);
   1.315 +
   1.316 +  // w2 = t >> 32;
   1.317 +  Node* w2 = phase->transform(new (phase->C) RShiftLNode(t, phase->intcon(N / 2)));
   1.318 +
   1.319 +  // w1 = u0*v1 + w1;
   1.320 +  Node* u0v1 = phase->transform(new (phase->C) MulLNode(u0, v1));
   1.321 +  w1         = phase->transform(new (phase->C) AddLNode(u0v1, w1));
   1.322 +
   1.323 +  // return u1*v1 + w2 + (w1 >> 32);
   1.324 +  Node* u1v1  = phase->transform(new (phase->C) MulLNode(u1, v1));
   1.325 +  Node* temp1 = phase->transform(new (phase->C) AddLNode(u1v1, w2));
   1.326 +  Node* temp2 = phase->transform(new (phase->C) RShiftLNode(w1, phase->intcon(N / 2)));
   1.327 +
   1.328 +  // Remove the bogus extra edges used to keep things alive
   1.329 +  PhaseIterGVN* igvn = phase->is_IterGVN();
   1.330 +  if (igvn != NULL) {
   1.331 +    igvn->remove_dead_node(hook);
   1.332 +  } else {
   1.333 +    for (int i = 0; i < 4; i++) {
   1.334 +      hook->set_req(i, NULL);
   1.335 +    }
   1.336 +  }
   1.337 +
   1.338 +  return new (phase->C) AddLNode(temp1, temp2);
   1.339 +}
   1.340 +
   1.341 +
   1.342 +//--------------------------transform_long_divide------------------------------
   1.343 +// Convert a division by constant divisor into an alternate Ideal graph.
   1.344 +// Return NULL if no transformation occurs.
   1.345 +static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {
   1.346 +  // Check for invalid divisors
   1.347 +  assert( divisor != 0L && divisor != min_jlong,
   1.348 +          "bad divisor for transforming to long multiply" );
   1.349 +
   1.350 +  bool d_pos = divisor >= 0;
   1.351 +  jlong d = d_pos ? divisor : -divisor;
   1.352 +  const int N = 64;
   1.353 +
   1.354 +  // Result
   1.355 +  Node *q = NULL;
   1.356 +
   1.357 +  if (d == 1) {
   1.358 +    // division by +/- 1
   1.359 +    if (!d_pos) {
   1.360 +      // Just negate the value
   1.361 +      q = new (phase->C) SubLNode(phase->longcon(0), dividend);
   1.362 +    }
   1.363 +  } else if ( is_power_of_2_long(d) ) {
   1.364 +
   1.365 +    // division by +/- a power of 2
   1.366 +
   1.367 +    // See if we can simply do a shift without rounding
   1.368 +    bool needs_rounding = true;
   1.369 +    const Type *dt = phase->type(dividend);
   1.370 +    const TypeLong *dtl = dt->isa_long();
   1.371 +
   1.372 +    if (dtl && dtl->_lo > 0) {
   1.373 +      // we don't need to round a positive dividend
   1.374 +      needs_rounding = false;
   1.375 +    } else if( dividend->Opcode() == Op_AndL ) {
   1.376 +      // An AND mask of sufficient size clears the low bits and
   1.377 +      // I can avoid rounding.
   1.378 +      const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();
   1.379 +      if( andconl_t && andconl_t->is_con() ) {
   1.380 +        jlong andconl = andconl_t->get_con();
   1.381 +        if( andconl < 0 && is_power_of_2_long(-andconl) && (-andconl) >= d ) {
   1.382 +          if( (-andconl) == d ) // Remove AND if it clears bits which will be shifted
   1.383 +            dividend = dividend->in(1);
   1.384 +          needs_rounding = false;
   1.385 +        }
   1.386 +      }
   1.387 +    }
   1.388 +
   1.389 +    // Add rounding to the shift to handle the sign bit
   1.390 +    int l = log2_long(d-1)+1;
   1.391 +    if (needs_rounding) {
   1.392 +      // Divide-by-power-of-2 can be made into a shift, but you have to do
   1.393 +      // more math for the rounding.  You need to add 0 for positive
   1.394 +      // numbers, and "i-1" for negative numbers.  Example: i=4, so the
   1.395 +      // shift is by 2.  You need to add 3 to negative dividends and 0 to
   1.396 +      // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
   1.397 +      // (-2+3)>>2 becomes 0, etc.
   1.398 +
   1.399 +      // Compute 0 or -1, based on sign bit
   1.400 +      Node *sign = phase->transform(new (phase->C) RShiftLNode(dividend, phase->intcon(N - 1)));
   1.401 +      // Mask sign bit to the low sign bits
   1.402 +      Node *round = phase->transform(new (phase->C) URShiftLNode(sign, phase->intcon(N - l)));
   1.403 +      // Round up before shifting
   1.404 +      dividend = phase->transform(new (phase->C) AddLNode(dividend, round));
   1.405 +    }
   1.406 +
   1.407 +    // Shift for division
   1.408 +    q = new (phase->C) RShiftLNode(dividend, phase->intcon(l));
   1.409 +
   1.410 +    if (!d_pos) {
   1.411 +      q = new (phase->C) SubLNode(phase->longcon(0), phase->transform(q));
   1.412 +    }
   1.413 +  } else if ( !Matcher::use_asm_for_ldiv_by_con(d) ) { // Use hardware DIV instruction when
   1.414 +                                                       // it is faster than code generated below.
   1.415 +    // Attempt the jlong constant divide -> multiply transform found in
   1.416 +    //   "Division by Invariant Integers using Multiplication"
   1.417 +    //     by Granlund and Montgomery
   1.418 +    // See also "Hacker's Delight", chapter 10 by Warren.
   1.419 +
   1.420 +    jlong magic_const;
   1.421 +    jint shift_const;
   1.422 +    if (magic_long_divide_constants(d, magic_const, shift_const)) {
   1.423 +      // Compute the high half of the dividend x magic multiplication
   1.424 +      Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
   1.425 +
   1.426 +      // The high half of the 128-bit multiply is computed.
   1.427 +      if (magic_const < 0) {
   1.428 +        // The magic multiplier is too large for a 64 bit constant. We've adjusted
   1.429 +        // it down by 2^64, but have to add 1 dividend back in after the multiplication.
   1.430 +        // This handles the "overflow" case described by Granlund and Montgomery.
   1.431 +        mul_hi = phase->transform(new (phase->C) AddLNode(dividend, mul_hi));
   1.432 +      }
   1.433 +
   1.434 +      // Shift over the (adjusted) mulhi
   1.435 +      if (shift_const != 0) {
   1.436 +        mul_hi = phase->transform(new (phase->C) RShiftLNode(mul_hi, phase->intcon(shift_const)));
   1.437 +      }
   1.438 +
   1.439 +      // Get a 0 or -1 from the sign of the dividend.
   1.440 +      Node *addend0 = mul_hi;
   1.441 +      Node *addend1 = phase->transform(new (phase->C) RShiftLNode(dividend, phase->intcon(N-1)));
   1.442 +
   1.443 +      // If the divisor is negative, swap the order of the input addends;
   1.444 +      // this has the effect of negating the quotient.
   1.445 +      if (!d_pos) {
   1.446 +        Node *temp = addend0; addend0 = addend1; addend1 = temp;
   1.447 +      }
   1.448 +
   1.449 +      // Adjust the final quotient by subtracting -1 (adding 1)
   1.450 +      // from the mul_hi.
   1.451 +      q = new (phase->C) SubLNode(addend0, addend1);
   1.452 +    }
   1.453 +  }
   1.454 +
   1.455 +  return q;
   1.456 +}
   1.457 +
   1.458 +//=============================================================================
   1.459 +//------------------------------Identity---------------------------------------
   1.460 +// If the divisor is 1, we are an identity on the dividend.
   1.461 +Node *DivINode::Identity( PhaseTransform *phase ) {
   1.462 +  return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
   1.463 +}
   1.464 +
   1.465 +//------------------------------Idealize---------------------------------------
   1.466 +// Divides can be changed to multiplies and/or shifts
   1.467 +Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
   1.468 +  if (in(0) && remove_dead_region(phase, can_reshape))  return this;
   1.469 +  // Don't bother trying to transform a dead node
   1.470 +  if( in(0) && in(0)->is_top() )  return NULL;
   1.471 +
   1.472 +  const Type *t = phase->type( in(2) );
   1.473 +  if( t == TypeInt::ONE )       // Identity?
   1.474 +    return NULL;                // Skip it
   1.475 +
   1.476 +  const TypeInt *ti = t->isa_int();
   1.477 +  if( !ti ) return NULL;
   1.478 +  if( !ti->is_con() ) return NULL;
   1.479 +  jint i = ti->get_con();       // Get divisor
   1.480 +
   1.481 +  if (i == 0) return NULL;      // Dividing by zero constant does not idealize
   1.482 +
   1.483 +  set_req(0,NULL);              // Dividing by a not-zero constant; no faulting
   1.484 +
   1.485 +  // Dividing by MININT does not optimize as a power-of-2 shift.
   1.486 +  if( i == min_jint ) return NULL;
   1.487 +
   1.488 +  return transform_int_divide( phase, in(1), i );
   1.489 +}
   1.490 +
   1.491 +//------------------------------Value------------------------------------------
   1.492 +// A DivINode divides its inputs.  The third input is a Control input, used to
   1.493 +// prevent hoisting the divide above an unsafe test.
   1.494 +const Type *DivINode::Value( PhaseTransform *phase ) const {
   1.495 +  // Either input is TOP ==> the result is TOP
   1.496 +  const Type *t1 = phase->type( in(1) );
   1.497 +  const Type *t2 = phase->type( in(2) );
   1.498 +  if( t1 == Type::TOP ) return Type::TOP;
   1.499 +  if( t2 == Type::TOP ) return Type::TOP;
   1.500 +
   1.501 +  // x/x == 1 since we always generate the dynamic divisor check for 0.
   1.502 +  if( phase->eqv( in(1), in(2) ) )
   1.503 +    return TypeInt::ONE;
   1.504 +
   1.505 +  // Either input is BOTTOM ==> the result is the local BOTTOM
   1.506 +  const Type *bot = bottom_type();
   1.507 +  if( (t1 == bot) || (t2 == bot) ||
   1.508 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
   1.509 +    return bot;
   1.510 +
   1.511 +  // Divide the two numbers.  We approximate.
   1.512 +  // If divisor is a constant and not zero
   1.513 +  const TypeInt *i1 = t1->is_int();
   1.514 +  const TypeInt *i2 = t2->is_int();
   1.515 +  int widen = MAX2(i1->_widen, i2->_widen);
   1.516 +
   1.517 +  if( i2->is_con() && i2->get_con() != 0 ) {
   1.518 +    int32 d = i2->get_con(); // Divisor
   1.519 +    jint lo, hi;
   1.520 +    if( d >= 0 ) {
   1.521 +      lo = i1->_lo/d;
   1.522 +      hi = i1->_hi/d;
   1.523 +    } else {
   1.524 +      if( d == -1 && i1->_lo == min_jint ) {
   1.525 +        // 'min_jint/-1' throws arithmetic exception during compilation
   1.526 +        lo = min_jint;
   1.527 +        // do not support holes, 'hi' must go to either min_jint or max_jint:
   1.528 +        // [min_jint, -10]/[-1,-1] ==> [min_jint] UNION [10,max_jint]
   1.529 +        hi = i1->_hi == min_jint ? min_jint : max_jint;
   1.530 +      } else {
   1.531 +        lo = i1->_hi/d;
   1.532 +        hi = i1->_lo/d;
   1.533 +      }
   1.534 +    }
   1.535 +    return TypeInt::make(lo, hi, widen);
   1.536 +  }
   1.537 +
   1.538 +  // If the dividend is a constant
   1.539 +  if( i1->is_con() ) {
   1.540 +    int32 d = i1->get_con();
   1.541 +    if( d < 0 ) {
   1.542 +      if( d == min_jint ) {
   1.543 +        //  (-min_jint) == min_jint == (min_jint / -1)
   1.544 +        return TypeInt::make(min_jint, max_jint/2 + 1, widen);
   1.545 +      } else {
   1.546 +        return TypeInt::make(d, -d, widen);
   1.547 +      }
   1.548 +    }
   1.549 +    return TypeInt::make(-d, d, widen);
   1.550 +  }
   1.551 +
   1.552 +  // Otherwise we give up all hope
   1.553 +  return TypeInt::INT;
   1.554 +}
   1.555 +
   1.556 +
   1.557 +//=============================================================================
   1.558 +//------------------------------Identity---------------------------------------
   1.559 +// If the divisor is 1, we are an identity on the dividend.
   1.560 +Node *DivLNode::Identity( PhaseTransform *phase ) {
   1.561 +  return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
   1.562 +}
   1.563 +
   1.564 +//------------------------------Idealize---------------------------------------
   1.565 +// Dividing by a power of 2 is a shift.
   1.566 +Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) {
   1.567 +  if (in(0) && remove_dead_region(phase, can_reshape))  return this;
   1.568 +  // Don't bother trying to transform a dead node
   1.569 +  if( in(0) && in(0)->is_top() )  return NULL;
   1.570 +
   1.571 +  const Type *t = phase->type( in(2) );
   1.572 +  if( t == TypeLong::ONE )      // Identity?
   1.573 +    return NULL;                // Skip it
   1.574 +
   1.575 +  const TypeLong *tl = t->isa_long();
   1.576 +  if( !tl ) return NULL;
   1.577 +  if( !tl->is_con() ) return NULL;
   1.578 +  jlong l = tl->get_con();      // Get divisor
   1.579 +
   1.580 +  if (l == 0) return NULL;      // Dividing by zero constant does not idealize
   1.581 +
   1.582 +  set_req(0,NULL);              // Dividing by a not-zero constant; no faulting
   1.583 +
   1.584 +  // Dividing by MINLONG does not optimize as a power-of-2 shift.
   1.585 +  if( l == min_jlong ) return NULL;
   1.586 +
   1.587 +  return transform_long_divide( phase, in(1), l );
   1.588 +}
   1.589 +
   1.590 +//------------------------------Value------------------------------------------
   1.591 +// A DivLNode divides its inputs.  The third input is a Control input, used to
   1.592 +// prevent hoisting the divide above an unsafe test.
   1.593 +const Type *DivLNode::Value( PhaseTransform *phase ) const {
   1.594 +  // Either input is TOP ==> the result is TOP
   1.595 +  const Type *t1 = phase->type( in(1) );
   1.596 +  const Type *t2 = phase->type( in(2) );
   1.597 +  if( t1 == Type::TOP ) return Type::TOP;
   1.598 +  if( t2 == Type::TOP ) return Type::TOP;
   1.599 +
   1.600 +  // x/x == 1 since we always generate the dynamic divisor check for 0.
   1.601 +  if( phase->eqv( in(1), in(2) ) )
   1.602 +    return TypeLong::ONE;
   1.603 +
   1.604 +  // Either input is BOTTOM ==> the result is the local BOTTOM
   1.605 +  const Type *bot = bottom_type();
   1.606 +  if( (t1 == bot) || (t2 == bot) ||
   1.607 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
   1.608 +    return bot;
   1.609 +
   1.610 +  // Divide the two numbers.  We approximate.
   1.611 +  // If divisor is a constant and not zero
   1.612 +  const TypeLong *i1 = t1->is_long();
   1.613 +  const TypeLong *i2 = t2->is_long();
   1.614 +  int widen = MAX2(i1->_widen, i2->_widen);
   1.615 +
   1.616 +  if( i2->is_con() && i2->get_con() != 0 ) {
   1.617 +    jlong d = i2->get_con();    // Divisor
   1.618 +    jlong lo, hi;
   1.619 +    if( d >= 0 ) {
   1.620 +      lo = i1->_lo/d;
   1.621 +      hi = i1->_hi/d;
   1.622 +    } else {
   1.623 +      if( d == CONST64(-1) && i1->_lo == min_jlong ) {
   1.624 +        // 'min_jlong/-1' throws arithmetic exception during compilation
   1.625 +        lo = min_jlong;
   1.626 +        // do not support holes, 'hi' must go to either min_jlong or max_jlong:
   1.627 +        // [min_jlong, -10]/[-1,-1] ==> [min_jlong] UNION [10,max_jlong]
   1.628 +        hi = i1->_hi == min_jlong ? min_jlong : max_jlong;
   1.629 +      } else {
   1.630 +        lo = i1->_hi/d;
   1.631 +        hi = i1->_lo/d;
   1.632 +      }
   1.633 +    }
   1.634 +    return TypeLong::make(lo, hi, widen);
   1.635 +  }
   1.636 +
   1.637 +  // If the dividend is a constant
   1.638 +  if( i1->is_con() ) {
   1.639 +    jlong d = i1->get_con();
   1.640 +    if( d < 0 ) {
   1.641 +      if( d == min_jlong ) {
   1.642 +        //  (-min_jlong) == min_jlong == (min_jlong / -1)
   1.643 +        return TypeLong::make(min_jlong, max_jlong/2 + 1, widen);
   1.644 +      } else {
   1.645 +        return TypeLong::make(d, -d, widen);
   1.646 +      }
   1.647 +    }
   1.648 +    return TypeLong::make(-d, d, widen);
   1.649 +  }
   1.650 +
   1.651 +  // Otherwise we give up all hope
   1.652 +  return TypeLong::LONG;
   1.653 +}
   1.654 +
   1.655 +
   1.656 +//=============================================================================
   1.657 +//------------------------------Value------------------------------------------
   1.658 +// An DivFNode divides its inputs.  The third input is a Control input, used to
   1.659 +// prevent hoisting the divide above an unsafe test.
   1.660 +const Type *DivFNode::Value( PhaseTransform *phase ) const {
   1.661 +  // Either input is TOP ==> the result is TOP
   1.662 +  const Type *t1 = phase->type( in(1) );
   1.663 +  const Type *t2 = phase->type( in(2) );
   1.664 +  if( t1 == Type::TOP ) return Type::TOP;
   1.665 +  if( t2 == Type::TOP ) return Type::TOP;
   1.666 +
   1.667 +  // Either input is BOTTOM ==> the result is the local BOTTOM
   1.668 +  const Type *bot = bottom_type();
   1.669 +  if( (t1 == bot) || (t2 == bot) ||
   1.670 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
   1.671 +    return bot;
   1.672 +
   1.673 +  // x/x == 1, we ignore 0/0.
   1.674 +  // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
   1.675 +  // Does not work for variables because of NaN's
   1.676 +  if( phase->eqv( in(1), in(2) ) && t1->base() == Type::FloatCon)
   1.677 +    if (!g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) // could be negative ZERO or NaN
   1.678 +      return TypeF::ONE;
   1.679 +
   1.680 +  if( t2 == TypeF::ONE )
   1.681 +    return t1;
   1.682 +
   1.683 +  // If divisor is a constant and not zero, divide them numbers
   1.684 +  if( t1->base() == Type::FloatCon &&
   1.685 +      t2->base() == Type::FloatCon &&
   1.686 +      t2->getf() != 0.0 ) // could be negative zero
   1.687 +    return TypeF::make( t1->getf()/t2->getf() );
   1.688 +
   1.689 +  // If the dividend is a constant zero
   1.690 +  // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
   1.691 +  // Test TypeF::ZERO is not sufficient as it could be negative zero
   1.692 +
   1.693 +  if( t1 == TypeF::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0 )
   1.694 +    return TypeF::ZERO;
   1.695 +
   1.696 +  // Otherwise we give up all hope
   1.697 +  return Type::FLOAT;
   1.698 +}
   1.699 +
   1.700 +//------------------------------isA_Copy---------------------------------------
   1.701 +// Dividing by self is 1.
   1.702 +// If the divisor is 1, we are an identity on the dividend.
   1.703 +Node *DivFNode::Identity( PhaseTransform *phase ) {
   1.704 +  return (phase->type( in(2) ) == TypeF::ONE) ? in(1) : this;
   1.705 +}
   1.706 +
   1.707 +
   1.708 +//------------------------------Idealize---------------------------------------
   1.709 +Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) {
   1.710 +  if (in(0) && remove_dead_region(phase, can_reshape))  return this;
   1.711 +  // Don't bother trying to transform a dead node
   1.712 +  if( in(0) && in(0)->is_top() )  return NULL;
   1.713 +
   1.714 +  const Type *t2 = phase->type( in(2) );
   1.715 +  if( t2 == TypeF::ONE )         // Identity?
   1.716 +    return NULL;                // Skip it
   1.717 +
   1.718 +  const TypeF *tf = t2->isa_float_constant();
   1.719 +  if( !tf ) return NULL;
   1.720 +  if( tf->base() != Type::FloatCon ) return NULL;
   1.721 +
   1.722 +  // Check for out of range values
   1.723 +  if( tf->is_nan() || !tf->is_finite() ) return NULL;
   1.724 +
   1.725 +  // Get the value
   1.726 +  float f = tf->getf();
   1.727 +  int exp;
   1.728 +
   1.729 +  // Only for special case of dividing by a power of 2
   1.730 +  if( frexp((double)f, &exp) != 0.5 ) return NULL;
   1.731 +
   1.732 +  // Limit the range of acceptable exponents
   1.733 +  if( exp < -126 || exp > 126 ) return NULL;
   1.734 +
   1.735 +  // Compute the reciprocal
   1.736 +  float reciprocal = ((float)1.0) / f;
   1.737 +
   1.738 +  assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
   1.739 +
   1.740 +  // return multiplication by the reciprocal
   1.741 +  return (new (phase->C) MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
   1.742 +}
   1.743 +
   1.744 +//=============================================================================
   1.745 +//------------------------------Value------------------------------------------
   1.746 +// An DivDNode divides its inputs.  The third input is a Control input, used to
   1.747 +// prevent hoisting the divide above an unsafe test.
   1.748 +const Type *DivDNode::Value( PhaseTransform *phase ) const {
   1.749 +  // Either input is TOP ==> the result is TOP
   1.750 +  const Type *t1 = phase->type( in(1) );
   1.751 +  const Type *t2 = phase->type( in(2) );
   1.752 +  if( t1 == Type::TOP ) return Type::TOP;
   1.753 +  if( t2 == Type::TOP ) return Type::TOP;
   1.754 +
   1.755 +  // Either input is BOTTOM ==> the result is the local BOTTOM
   1.756 +  const Type *bot = bottom_type();
   1.757 +  if( (t1 == bot) || (t2 == bot) ||
   1.758 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
   1.759 +    return bot;
   1.760 +
   1.761 +  // x/x == 1, we ignore 0/0.
   1.762 +  // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
   1.763 +  // Does not work for variables because of NaN's
   1.764 +  if( phase->eqv( in(1), in(2) ) && t1->base() == Type::DoubleCon)
   1.765 +    if (!g_isnan(t1->getd()) && g_isfinite(t1->getd()) && t1->getd() != 0.0) // could be negative ZERO or NaN
   1.766 +      return TypeD::ONE;
   1.767 +
   1.768 +  if( t2 == TypeD::ONE )
   1.769 +    return t1;
   1.770 +
   1.771 +#if defined(IA32)
   1.772 +  if (!phase->C->method()->is_strict())
   1.773 +    // Can't trust native compilers to properly fold strict double
   1.774 +    // division with round-to-zero on this platform.
   1.775 +#endif
   1.776 +    {
   1.777 +      // If divisor is a constant and not zero, divide them numbers
   1.778 +      if( t1->base() == Type::DoubleCon &&
   1.779 +          t2->base() == Type::DoubleCon &&
   1.780 +          t2->getd() != 0.0 ) // could be negative zero
   1.781 +        return TypeD::make( t1->getd()/t2->getd() );
   1.782 +    }
   1.783 +
   1.784 +  // If the dividend is a constant zero
   1.785 +  // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
   1.786 +  // Test TypeF::ZERO is not sufficient as it could be negative zero
   1.787 +  if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )
   1.788 +    return TypeD::ZERO;
   1.789 +
   1.790 +  // Otherwise we give up all hope
   1.791 +  return Type::DOUBLE;
   1.792 +}
   1.793 +
   1.794 +
   1.795 +//------------------------------isA_Copy---------------------------------------
   1.796 +// Dividing by self is 1.
   1.797 +// If the divisor is 1, we are an identity on the dividend.
   1.798 +Node *DivDNode::Identity( PhaseTransform *phase ) {
   1.799 +  return (phase->type( in(2) ) == TypeD::ONE) ? in(1) : this;
   1.800 +}
   1.801 +
   1.802 +//------------------------------Idealize---------------------------------------
   1.803 +Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) {
   1.804 +  if (in(0) && remove_dead_region(phase, can_reshape))  return this;
   1.805 +  // Don't bother trying to transform a dead node
   1.806 +  if( in(0) && in(0)->is_top() )  return NULL;
   1.807 +
   1.808 +  const Type *t2 = phase->type( in(2) );
   1.809 +  if( t2 == TypeD::ONE )         // Identity?
   1.810 +    return NULL;                // Skip it
   1.811 +
   1.812 +  const TypeD *td = t2->isa_double_constant();
   1.813 +  if( !td ) return NULL;
   1.814 +  if( td->base() != Type::DoubleCon ) return NULL;
   1.815 +
   1.816 +  // Check for out of range values
   1.817 +  if( td->is_nan() || !td->is_finite() ) return NULL;
   1.818 +
   1.819 +  // Get the value
   1.820 +  double d = td->getd();
   1.821 +  int exp;
   1.822 +
   1.823 +  // Only for special case of dividing by a power of 2
   1.824 +  if( frexp(d, &exp) != 0.5 ) return NULL;
   1.825 +
   1.826 +  // Limit the range of acceptable exponents
   1.827 +  if( exp < -1021 || exp > 1022 ) return NULL;
   1.828 +
   1.829 +  // Compute the reciprocal
   1.830 +  double reciprocal = 1.0 / d;
   1.831 +
   1.832 +  assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
   1.833 +
   1.834 +  // return multiplication by the reciprocal
   1.835 +  return (new (phase->C) MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
   1.836 +}
   1.837 +
   1.838 +//=============================================================================
   1.839 +//------------------------------Idealize---------------------------------------
   1.840 +Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
   1.841 +  // Check for dead control input
   1.842 +  if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
   1.843 +  // Don't bother trying to transform a dead node
   1.844 +  if( in(0) && in(0)->is_top() )  return NULL;
   1.845 +
   1.846 +  // Get the modulus
   1.847 +  const Type *t = phase->type( in(2) );
   1.848 +  if( t == Type::TOP ) return NULL;
   1.849 +  const TypeInt *ti = t->is_int();
   1.850 +
   1.851 +  // Check for useless control input
   1.852 +  // Check for excluding mod-zero case
   1.853 +  if( in(0) && (ti->_hi < 0 || ti->_lo > 0) ) {
   1.854 +    set_req(0, NULL);        // Yank control input
   1.855 +    return this;
   1.856 +  }
   1.857 +
   1.858 +  // See if we are MOD'ing by 2^k or 2^k-1.
   1.859 +  if( !ti->is_con() ) return NULL;
   1.860 +  jint con = ti->get_con();
   1.861 +
   1.862 +  Node *hook = new (phase->C) Node(1);
   1.863 +
   1.864 +  // First, special check for modulo 2^k-1
   1.865 +  if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
   1.866 +    uint k = exact_log2(con+1);  // Extract k
   1.867 +
   1.868 +    // Basic algorithm by David Detlefs.  See fastmod_int.java for gory details.
   1.869 +    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*/};
   1.870 +    int trip_count = 1;
   1.871 +    if( k < ARRAY_SIZE(unroll_factor))  trip_count = unroll_factor[k];
   1.872 +
   1.873 +    // If the unroll factor is not too large, and if conditional moves are
   1.874 +    // ok, then use this case
   1.875 +    if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
   1.876 +      Node *x = in(1);            // Value being mod'd
   1.877 +      Node *divisor = in(2);      // Also is mask
   1.878 +
   1.879 +      hook->init_req(0, x);       // Add a use to x to prevent him from dying
   1.880 +      // Generate code to reduce X rapidly to nearly 2^k-1.
   1.881 +      for( int i = 0; i < trip_count; i++ ) {
   1.882 +        Node *xl = phase->transform( new (phase->C) AndINode(x,divisor) );
   1.883 +        Node *xh = phase->transform( new (phase->C) RShiftINode(x,phase->intcon(k)) ); // Must be signed
   1.884 +        x = phase->transform( new (phase->C) AddINode(xh,xl) );
   1.885 +        hook->set_req(0, x);
   1.886 +      }
   1.887 +
   1.888 +      // Generate sign-fixup code.  Was original value positive?
   1.889 +      // int hack_res = (i >= 0) ? divisor : 1;
   1.890 +      Node *cmp1 = phase->transform( new (phase->C) CmpINode( in(1), phase->intcon(0) ) );
   1.891 +      Node *bol1 = phase->transform( new (phase->C) BoolNode( cmp1, BoolTest::ge ) );
   1.892 +      Node *cmov1= phase->transform( new (phase->C) CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
   1.893 +      // if( x >= hack_res ) x -= divisor;
   1.894 +      Node *sub  = phase->transform( new (phase->C) SubINode( x, divisor ) );
   1.895 +      Node *cmp2 = phase->transform( new (phase->C) CmpINode( x, cmov1 ) );
   1.896 +      Node *bol2 = phase->transform( new (phase->C) BoolNode( cmp2, BoolTest::ge ) );
   1.897 +      // Convention is to not transform the return value of an Ideal
   1.898 +      // since Ideal is expected to return a modified 'this' or a new node.
   1.899 +      Node *cmov2= new (phase->C) CMoveINode(bol2, x, sub, TypeInt::INT);
   1.900 +      // cmov2 is now the mod
   1.901 +
   1.902 +      // Now remove the bogus extra edges used to keep things alive
   1.903 +      if (can_reshape) {
   1.904 +        phase->is_IterGVN()->remove_dead_node(hook);
   1.905 +      } else {
   1.906 +        hook->set_req(0, NULL);   // Just yank bogus edge during Parse phase
   1.907 +      }
   1.908 +      return cmov2;
   1.909 +    }
   1.910 +  }
   1.911 +
   1.912 +  // Fell thru, the unroll case is not appropriate. Transform the modulo
   1.913 +  // into a long multiply/int multiply/subtract case
   1.914 +
   1.915 +  // Cannot handle mod 0, and min_jint isn't handled by the transform
   1.916 +  if( con == 0 || con == min_jint ) return NULL;
   1.917 +
   1.918 +  // Get the absolute value of the constant; at this point, we can use this
   1.919 +  jint pos_con = (con >= 0) ? con : -con;
   1.920 +
   1.921 +  // integer Mod 1 is always 0
   1.922 +  if( pos_con == 1 ) return new (phase->C) ConINode(TypeInt::ZERO);
   1.923 +
   1.924 +  int log2_con = -1;
   1.925 +
   1.926 +  // If this is a power of two, they maybe we can mask it
   1.927 +  if( is_power_of_2(pos_con) ) {
   1.928 +    log2_con = log2_intptr((intptr_t)pos_con);
   1.929 +
   1.930 +    const Type *dt = phase->type(in(1));
   1.931 +    const TypeInt *dti = dt->isa_int();
   1.932 +
   1.933 +    // See if this can be masked, if the dividend is non-negative
   1.934 +    if( dti && dti->_lo >= 0 )
   1.935 +      return ( new (phase->C) AndINode( in(1), phase->intcon( pos_con-1 ) ) );
   1.936 +  }
   1.937 +
   1.938 +  // Save in(1) so that it cannot be changed or deleted
   1.939 +  hook->init_req(0, in(1));
   1.940 +
   1.941 +  // Divide using the transform from DivI to MulL
   1.942 +  Node *result = transform_int_divide( phase, in(1), pos_con );
   1.943 +  if (result != NULL) {
   1.944 +    Node *divide = phase->transform(result);
   1.945 +
   1.946 +    // Re-multiply, using a shift if this is a power of two
   1.947 +    Node *mult = NULL;
   1.948 +
   1.949 +    if( log2_con >= 0 )
   1.950 +      mult = phase->transform( new (phase->C) LShiftINode( divide, phase->intcon( log2_con ) ) );
   1.951 +    else
   1.952 +      mult = phase->transform( new (phase->C) MulINode( divide, phase->intcon( pos_con ) ) );
   1.953 +
   1.954 +    // Finally, subtract the multiplied divided value from the original
   1.955 +    result = new (phase->C) SubINode( in(1), mult );
   1.956 +  }
   1.957 +
   1.958 +  // Now remove the bogus extra edges used to keep things alive
   1.959 +  if (can_reshape) {
   1.960 +    phase->is_IterGVN()->remove_dead_node(hook);
   1.961 +  } else {
   1.962 +    hook->set_req(0, NULL);       // Just yank bogus edge during Parse phase
   1.963 +  }
   1.964 +
   1.965 +  // return the value
   1.966 +  return result;
   1.967 +}
   1.968 +
   1.969 +//------------------------------Value------------------------------------------
   1.970 +const Type *ModINode::Value( PhaseTransform *phase ) const {
   1.971 +  // Either input is TOP ==> the result is TOP
   1.972 +  const Type *t1 = phase->type( in(1) );
   1.973 +  const Type *t2 = phase->type( in(2) );
   1.974 +  if( t1 == Type::TOP ) return Type::TOP;
   1.975 +  if( t2 == Type::TOP ) return Type::TOP;
   1.976 +
   1.977 +  // We always generate the dynamic check for 0.
   1.978 +  // 0 MOD X is 0
   1.979 +  if( t1 == TypeInt::ZERO ) return TypeInt::ZERO;
   1.980 +  // X MOD X is 0
   1.981 +  if( phase->eqv( in(1), in(2) ) ) return TypeInt::ZERO;
   1.982 +
   1.983 +  // Either input is BOTTOM ==> the result is the local BOTTOM
   1.984 +  const Type *bot = bottom_type();
   1.985 +  if( (t1 == bot) || (t2 == bot) ||
   1.986 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
   1.987 +    return bot;
   1.988 +
   1.989 +  const TypeInt *i1 = t1->is_int();
   1.990 +  const TypeInt *i2 = t2->is_int();
   1.991 +  if( !i1->is_con() || !i2->is_con() ) {
   1.992 +    if( i1->_lo >= 0 && i2->_lo >= 0 )
   1.993 +      return TypeInt::POS;
   1.994 +    // If both numbers are not constants, we know little.
   1.995 +    return TypeInt::INT;
   1.996 +  }
   1.997 +  // Mod by zero?  Throw exception at runtime!
   1.998 +  if( !i2->get_con() ) return TypeInt::POS;
   1.999 +
  1.1000 +  // We must be modulo'ing 2 float constants.
  1.1001 +  // Check for min_jint % '-1', result is defined to be '0'.
  1.1002 +  if( i1->get_con() == min_jint && i2->get_con() == -1 )
  1.1003 +    return TypeInt::ZERO;
  1.1004 +
  1.1005 +  return TypeInt::make( i1->get_con() % i2->get_con() );
  1.1006 +}
  1.1007 +
  1.1008 +
  1.1009 +//=============================================================================
  1.1010 +//------------------------------Idealize---------------------------------------
  1.1011 +Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
  1.1012 +  // Check for dead control input
  1.1013 +  if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
  1.1014 +  // Don't bother trying to transform a dead node
  1.1015 +  if( in(0) && in(0)->is_top() )  return NULL;
  1.1016 +
  1.1017 +  // Get the modulus
  1.1018 +  const Type *t = phase->type( in(2) );
  1.1019 +  if( t == Type::TOP ) return NULL;
  1.1020 +  const TypeLong *tl = t->is_long();
  1.1021 +
  1.1022 +  // Check for useless control input
  1.1023 +  // Check for excluding mod-zero case
  1.1024 +  if( in(0) && (tl->_hi < 0 || tl->_lo > 0) ) {
  1.1025 +    set_req(0, NULL);        // Yank control input
  1.1026 +    return this;
  1.1027 +  }
  1.1028 +
  1.1029 +  // See if we are MOD'ing by 2^k or 2^k-1.
  1.1030 +  if( !tl->is_con() ) return NULL;
  1.1031 +  jlong con = tl->get_con();
  1.1032 +
  1.1033 +  Node *hook = new (phase->C) Node(1);
  1.1034 +
  1.1035 +  // Expand mod
  1.1036 +  if( con >= 0 && con < max_jlong && is_power_of_2_long(con+1) ) {
  1.1037 +    uint k = exact_log2_long(con+1);  // Extract k
  1.1038 +
  1.1039 +    // Basic algorithm by David Detlefs.  See fastmod_long.java for gory details.
  1.1040 +    // Used to help a popular random number generator which does a long-mod
  1.1041 +    // of 2^31-1 and shows up in SpecJBB and SciMark.
  1.1042 +    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*/};
  1.1043 +    int trip_count = 1;
  1.1044 +    if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
  1.1045 +
  1.1046 +    // If the unroll factor is not too large, and if conditional moves are
  1.1047 +    // ok, then use this case
  1.1048 +    if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
  1.1049 +      Node *x = in(1);            // Value being mod'd
  1.1050 +      Node *divisor = in(2);      // Also is mask
  1.1051 +
  1.1052 +      hook->init_req(0, x);       // Add a use to x to prevent him from dying
  1.1053 +      // Generate code to reduce X rapidly to nearly 2^k-1.
  1.1054 +      for( int i = 0; i < trip_count; i++ ) {
  1.1055 +        Node *xl = phase->transform( new (phase->C) AndLNode(x,divisor) );
  1.1056 +        Node *xh = phase->transform( new (phase->C) RShiftLNode(x,phase->intcon(k)) ); // Must be signed
  1.1057 +        x = phase->transform( new (phase->C) AddLNode(xh,xl) );
  1.1058 +        hook->set_req(0, x);    // Add a use to x to prevent him from dying
  1.1059 +      }
  1.1060 +
  1.1061 +      // Generate sign-fixup code.  Was original value positive?
  1.1062 +      // long hack_res = (i >= 0) ? divisor : CONST64(1);
  1.1063 +      Node *cmp1 = phase->transform( new (phase->C) CmpLNode( in(1), phase->longcon(0) ) );
  1.1064 +      Node *bol1 = phase->transform( new (phase->C) BoolNode( cmp1, BoolTest::ge ) );
  1.1065 +      Node *cmov1= phase->transform( new (phase->C) CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
  1.1066 +      // if( x >= hack_res ) x -= divisor;
  1.1067 +      Node *sub  = phase->transform( new (phase->C) SubLNode( x, divisor ) );
  1.1068 +      Node *cmp2 = phase->transform( new (phase->C) CmpLNode( x, cmov1 ) );
  1.1069 +      Node *bol2 = phase->transform( new (phase->C) BoolNode( cmp2, BoolTest::ge ) );
  1.1070 +      // Convention is to not transform the return value of an Ideal
  1.1071 +      // since Ideal is expected to return a modified 'this' or a new node.
  1.1072 +      Node *cmov2= new (phase->C) CMoveLNode(bol2, x, sub, TypeLong::LONG);
  1.1073 +      // cmov2 is now the mod
  1.1074 +
  1.1075 +      // Now remove the bogus extra edges used to keep things alive
  1.1076 +      if (can_reshape) {
  1.1077 +        phase->is_IterGVN()->remove_dead_node(hook);
  1.1078 +      } else {
  1.1079 +        hook->set_req(0, NULL);   // Just yank bogus edge during Parse phase
  1.1080 +      }
  1.1081 +      return cmov2;
  1.1082 +    }
  1.1083 +  }
  1.1084 +
  1.1085 +  // Fell thru, the unroll case is not appropriate. Transform the modulo
  1.1086 +  // into a long multiply/int multiply/subtract case
  1.1087 +
  1.1088 +  // Cannot handle mod 0, and min_jlong isn't handled by the transform
  1.1089 +  if( con == 0 || con == min_jlong ) return NULL;
  1.1090 +
  1.1091 +  // Get the absolute value of the constant; at this point, we can use this
  1.1092 +  jlong pos_con = (con >= 0) ? con : -con;
  1.1093 +
  1.1094 +  // integer Mod 1 is always 0
  1.1095 +  if( pos_con == 1 ) return new (phase->C) ConLNode(TypeLong::ZERO);
  1.1096 +
  1.1097 +  int log2_con = -1;
  1.1098 +
  1.1099 +  // If this is a power of two, then maybe we can mask it
  1.1100 +  if( is_power_of_2_long(pos_con) ) {
  1.1101 +    log2_con = exact_log2_long(pos_con);
  1.1102 +
  1.1103 +    const Type *dt = phase->type(in(1));
  1.1104 +    const TypeLong *dtl = dt->isa_long();
  1.1105 +
  1.1106 +    // See if this can be masked, if the dividend is non-negative
  1.1107 +    if( dtl && dtl->_lo >= 0 )
  1.1108 +      return ( new (phase->C) AndLNode( in(1), phase->longcon( pos_con-1 ) ) );
  1.1109 +  }
  1.1110 +
  1.1111 +  // Save in(1) so that it cannot be changed or deleted
  1.1112 +  hook->init_req(0, in(1));
  1.1113 +
  1.1114 +  // Divide using the transform from DivL to MulL
  1.1115 +  Node *result = transform_long_divide( phase, in(1), pos_con );
  1.1116 +  if (result != NULL) {
  1.1117 +    Node *divide = phase->transform(result);
  1.1118 +
  1.1119 +    // Re-multiply, using a shift if this is a power of two
  1.1120 +    Node *mult = NULL;
  1.1121 +
  1.1122 +    if( log2_con >= 0 )
  1.1123 +      mult = phase->transform( new (phase->C) LShiftLNode( divide, phase->intcon( log2_con ) ) );
  1.1124 +    else
  1.1125 +      mult = phase->transform( new (phase->C) MulLNode( divide, phase->longcon( pos_con ) ) );
  1.1126 +
  1.1127 +    // Finally, subtract the multiplied divided value from the original
  1.1128 +    result = new (phase->C) SubLNode( in(1), mult );
  1.1129 +  }
  1.1130 +
  1.1131 +  // Now remove the bogus extra edges used to keep things alive
  1.1132 +  if (can_reshape) {
  1.1133 +    phase->is_IterGVN()->remove_dead_node(hook);
  1.1134 +  } else {
  1.1135 +    hook->set_req(0, NULL);       // Just yank bogus edge during Parse phase
  1.1136 +  }
  1.1137 +
  1.1138 +  // return the value
  1.1139 +  return result;
  1.1140 +}
  1.1141 +
  1.1142 +//------------------------------Value------------------------------------------
  1.1143 +const Type *ModLNode::Value( PhaseTransform *phase ) const {
  1.1144 +  // Either input is TOP ==> the result is TOP
  1.1145 +  const Type *t1 = phase->type( in(1) );
  1.1146 +  const Type *t2 = phase->type( in(2) );
  1.1147 +  if( t1 == Type::TOP ) return Type::TOP;
  1.1148 +  if( t2 == Type::TOP ) return Type::TOP;
  1.1149 +
  1.1150 +  // We always generate the dynamic check for 0.
  1.1151 +  // 0 MOD X is 0
  1.1152 +  if( t1 == TypeLong::ZERO ) return TypeLong::ZERO;
  1.1153 +  // X MOD X is 0
  1.1154 +  if( phase->eqv( in(1), in(2) ) ) return TypeLong::ZERO;
  1.1155 +
  1.1156 +  // Either input is BOTTOM ==> the result is the local BOTTOM
  1.1157 +  const Type *bot = bottom_type();
  1.1158 +  if( (t1 == bot) || (t2 == bot) ||
  1.1159 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
  1.1160 +    return bot;
  1.1161 +
  1.1162 +  const TypeLong *i1 = t1->is_long();
  1.1163 +  const TypeLong *i2 = t2->is_long();
  1.1164 +  if( !i1->is_con() || !i2->is_con() ) {
  1.1165 +    if( i1->_lo >= CONST64(0) && i2->_lo >= CONST64(0) )
  1.1166 +      return TypeLong::POS;
  1.1167 +    // If both numbers are not constants, we know little.
  1.1168 +    return TypeLong::LONG;
  1.1169 +  }
  1.1170 +  // Mod by zero?  Throw exception at runtime!
  1.1171 +  if( !i2->get_con() ) return TypeLong::POS;
  1.1172 +
  1.1173 +  // We must be modulo'ing 2 float constants.
  1.1174 +  // Check for min_jint % '-1', result is defined to be '0'.
  1.1175 +  if( i1->get_con() == min_jlong && i2->get_con() == -1 )
  1.1176 +    return TypeLong::ZERO;
  1.1177 +
  1.1178 +  return TypeLong::make( i1->get_con() % i2->get_con() );
  1.1179 +}
  1.1180 +
  1.1181 +
  1.1182 +//=============================================================================
  1.1183 +//------------------------------Value------------------------------------------
  1.1184 +const Type *ModFNode::Value( PhaseTransform *phase ) const {
  1.1185 +  // Either input is TOP ==> the result is TOP
  1.1186 +  const Type *t1 = phase->type( in(1) );
  1.1187 +  const Type *t2 = phase->type( in(2) );
  1.1188 +  if( t1 == Type::TOP ) return Type::TOP;
  1.1189 +  if( t2 == Type::TOP ) return Type::TOP;
  1.1190 +
  1.1191 +  // Either input is BOTTOM ==> the result is the local BOTTOM
  1.1192 +  const Type *bot = bottom_type();
  1.1193 +  if( (t1 == bot) || (t2 == bot) ||
  1.1194 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
  1.1195 +    return bot;
  1.1196 +
  1.1197 +  // If either number is not a constant, we know nothing.
  1.1198 +  if ((t1->base() != Type::FloatCon) || (t2->base() != Type::FloatCon)) {
  1.1199 +    return Type::FLOAT;         // note: x%x can be either NaN or 0
  1.1200 +  }
  1.1201 +
  1.1202 +  float f1 = t1->getf();
  1.1203 +  float f2 = t2->getf();
  1.1204 +  jint  x1 = jint_cast(f1);     // note:  *(int*)&f1, not just (int)f1
  1.1205 +  jint  x2 = jint_cast(f2);
  1.1206 +
  1.1207 +  // If either is a NaN, return an input NaN
  1.1208 +  if (g_isnan(f1))    return t1;
  1.1209 +  if (g_isnan(f2))    return t2;
  1.1210 +
  1.1211 +  // If an operand is infinity or the divisor is +/- zero, punt.
  1.1212 +  if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jint)
  1.1213 +    return Type::FLOAT;
  1.1214 +
  1.1215 +  // We must be modulo'ing 2 float constants.
  1.1216 +  // Make sure that the sign of the fmod is equal to the sign of the dividend
  1.1217 +  jint xr = jint_cast(fmod(f1, f2));
  1.1218 +  if ((x1 ^ xr) < 0) {
  1.1219 +    xr ^= min_jint;
  1.1220 +  }
  1.1221 +
  1.1222 +  return TypeF::make(jfloat_cast(xr));
  1.1223 +}
  1.1224 +
  1.1225 +
  1.1226 +//=============================================================================
  1.1227 +//------------------------------Value------------------------------------------
  1.1228 +const Type *ModDNode::Value( PhaseTransform *phase ) const {
  1.1229 +  // Either input is TOP ==> the result is TOP
  1.1230 +  const Type *t1 = phase->type( in(1) );
  1.1231 +  const Type *t2 = phase->type( in(2) );
  1.1232 +  if( t1 == Type::TOP ) return Type::TOP;
  1.1233 +  if( t2 == Type::TOP ) return Type::TOP;
  1.1234 +
  1.1235 +  // Either input is BOTTOM ==> the result is the local BOTTOM
  1.1236 +  const Type *bot = bottom_type();
  1.1237 +  if( (t1 == bot) || (t2 == bot) ||
  1.1238 +      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
  1.1239 +    return bot;
  1.1240 +
  1.1241 +  // If either number is not a constant, we know nothing.
  1.1242 +  if ((t1->base() != Type::DoubleCon) || (t2->base() != Type::DoubleCon)) {
  1.1243 +    return Type::DOUBLE;        // note: x%x can be either NaN or 0
  1.1244 +  }
  1.1245 +
  1.1246 +  double f1 = t1->getd();
  1.1247 +  double f2 = t2->getd();
  1.1248 +  jlong  x1 = jlong_cast(f1);   // note:  *(long*)&f1, not just (long)f1
  1.1249 +  jlong  x2 = jlong_cast(f2);
  1.1250 +
  1.1251 +  // If either is a NaN, return an input NaN
  1.1252 +  if (g_isnan(f1))    return t1;
  1.1253 +  if (g_isnan(f2))    return t2;
  1.1254 +
  1.1255 +  // If an operand is infinity or the divisor is +/- zero, punt.
  1.1256 +  if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jlong)
  1.1257 +    return Type::DOUBLE;
  1.1258 +
  1.1259 +  // We must be modulo'ing 2 double constants.
  1.1260 +  // Make sure that the sign of the fmod is equal to the sign of the dividend
  1.1261 +  jlong xr = jlong_cast(fmod(f1, f2));
  1.1262 +  if ((x1 ^ xr) < 0) {
  1.1263 +    xr ^= min_jlong;
  1.1264 +  }
  1.1265 +
  1.1266 +  return TypeD::make(jdouble_cast(xr));
  1.1267 +}
  1.1268 +
  1.1269 +//=============================================================================
  1.1270 +
  1.1271 +DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
  1.1272 +  init_req(0, c);
  1.1273 +  init_req(1, dividend);
  1.1274 +  init_req(2, divisor);
  1.1275 +}
  1.1276 +
  1.1277 +//------------------------------make------------------------------------------
  1.1278 +DivModINode* DivModINode::make(Compile* C, Node* div_or_mod) {
  1.1279 +  Node* n = div_or_mod;
  1.1280 +  assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
  1.1281 +         "only div or mod input pattern accepted");
  1.1282 +
  1.1283 +  DivModINode* divmod = new (C) DivModINode(n->in(0), n->in(1), n->in(2));
  1.1284 +  Node*        dproj  = new (C) ProjNode(divmod, DivModNode::div_proj_num);
  1.1285 +  Node*        mproj  = new (C) ProjNode(divmod, DivModNode::mod_proj_num);
  1.1286 +  return divmod;
  1.1287 +}
  1.1288 +
  1.1289 +//------------------------------make------------------------------------------
  1.1290 +DivModLNode* DivModLNode::make(Compile* C, Node* div_or_mod) {
  1.1291 +  Node* n = div_or_mod;
  1.1292 +  assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
  1.1293 +         "only div or mod input pattern accepted");
  1.1294 +
  1.1295 +  DivModLNode* divmod = new (C) DivModLNode(n->in(0), n->in(1), n->in(2));
  1.1296 +  Node*        dproj  = new (C) ProjNode(divmod, DivModNode::div_proj_num);
  1.1297 +  Node*        mproj  = new (C) ProjNode(divmod, DivModNode::mod_proj_num);
  1.1298 +  return divmod;
  1.1299 +}
  1.1300 +
  1.1301 +//------------------------------match------------------------------------------
  1.1302 +// return result(s) along with their RegMask info
  1.1303 +Node *DivModINode::match( const ProjNode *proj, const Matcher *match ) {
  1.1304 +  uint ideal_reg = proj->ideal_reg();
  1.1305 +  RegMask rm;
  1.1306 +  if (proj->_con == div_proj_num) {
  1.1307 +    rm = match->divI_proj_mask();
  1.1308 +  } else {
  1.1309 +    assert(proj->_con == mod_proj_num, "must be div or mod projection");
  1.1310 +    rm = match->modI_proj_mask();
  1.1311 +  }
  1.1312 +  return new (match->C)MachProjNode(this, proj->_con, rm, ideal_reg);
  1.1313 +}
  1.1314 +
  1.1315 +
  1.1316 +//------------------------------match------------------------------------------
  1.1317 +// return result(s) along with their RegMask info
  1.1318 +Node *DivModLNode::match( const ProjNode *proj, const Matcher *match ) {
  1.1319 +  uint ideal_reg = proj->ideal_reg();
  1.1320 +  RegMask rm;
  1.1321 +  if (proj->_con == div_proj_num) {
  1.1322 +    rm = match->divL_proj_mask();
  1.1323 +  } else {
  1.1324 +    assert(proj->_con == mod_proj_num, "must be div or mod projection");
  1.1325 +    rm = match->modL_proj_mask();
  1.1326 +  }
  1.1327 +  return new (match->C)MachProjNode(this, proj->_con, rm, ideal_reg);
  1.1328 +}

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