1 /*
   2  * Copyright (c) 1997, 2021, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.
   8  *
   9  * This code is distributed in the hope that it will be useful, but WITHOUT
  10  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  11  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  12  * version 2 for more details (a copy is included in the LICENSE file that
  13  * accompanied this code).
  14  *
  15  * You should have received a copy of the GNU General Public License version
  16  * 2 along with this work; if not, write to the Free Software Foundation,
  17  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  18  *
  19  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  20  * or visit www.oracle.com if you need additional information or have any
  21  * questions.
  22  *
  23  */
  24 
  25 #include "precompiled.hpp"
  26 #include "memory/allocation.inline.hpp"
  27 #include "opto/addnode.hpp"
  28 #include "opto/connode.hpp"
  29 #include "opto/convertnode.hpp"
  30 #include "opto/divnode.hpp"
  31 #include "opto/machnode.hpp"
  32 #include "opto/movenode.hpp"
  33 #include "opto/matcher.hpp"
  34 #include "opto/mulnode.hpp"
  35 #include "opto/phaseX.hpp"
  36 #include "opto/subnode.hpp"
  37 #include "utilities/powerOfTwo.hpp"
  38 
  39 // Portions of code courtesy of Clifford Click
  40 
  41 // Optimization - Graph Style
  42 
  43 #include <math.h>
  44 
  45 //----------------------magic_int_divide_constants-----------------------------
  46 // Compute magic multiplier and shift constant for converting a 32 bit divide
  47 // by constant into a multiply/shift/add series. Return false if calculations
  48 // fail.
  49 //
  50 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
  51 // minor type name and parameter changes.
  52 static bool magic_int_divide_constants(jint d, jint &M, jint &s) {
  53   int32_t p;
  54   uint32_t ad, anc, delta, q1, r1, q2, r2, t;
  55   const uint32_t two31 = 0x80000000L;     // 2**31.
  56 
  57   ad = ABS(d);
  58   if (d == 0 || d == 1) return false;
  59   t = two31 + ((uint32_t)d >> 31);
  60   anc = t - 1 - t%ad;     // Absolute value of nc.
  61   p = 31;                 // Init. p.
  62   q1 = two31/anc;         // Init. q1 = 2**p/|nc|.
  63   r1 = two31 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
  64   q2 = two31/ad;          // Init. q2 = 2**p/|d|.
  65   r2 = two31 - q2*ad;     // Init. r2 = rem(2**p, |d|).
  66   do {
  67     p = p + 1;
  68     q1 = 2*q1;            // Update q1 = 2**p/|nc|.
  69     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
  70     if (r1 >= anc) {      // (Must be an unsigned
  71       q1 = q1 + 1;        // comparison here).
  72       r1 = r1 - anc;
  73     }
  74     q2 = 2*q2;            // Update q2 = 2**p/|d|.
  75     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
  76     if (r2 >= ad) {       // (Must be an unsigned
  77       q2 = q2 + 1;        // comparison here).
  78       r2 = r2 - ad;
  79     }
  80     delta = ad - r2;
  81   } while (q1 < delta || (q1 == delta && r1 == 0));
  82 
  83   M = q2 + 1;
  84   if (d < 0) M = -M;      // Magic number and
  85   s = p - 32;             // shift amount to return.
  86 
  87   return true;
  88 }
  89 
  90 //--------------------------transform_int_divide-------------------------------
  91 // Convert a division by constant divisor into an alternate Ideal graph.
  92 // Return NULL if no transformation occurs.
  93 static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) {
  94 
  95   // Check for invalid divisors
  96   assert( divisor != 0 && divisor != min_jint,
  97           "bad divisor for transforming to long multiply" );
  98 
  99   bool d_pos = divisor >= 0;
 100   jint d = d_pos ? divisor : -divisor;
 101   const int N = 32;
 102 
 103   // Result
 104   Node *q = NULL;
 105 
 106   if (d == 1) {
 107     // division by +/- 1
 108     if (!d_pos) {
 109       // Just negate the value
 110       q = new SubINode(phase->intcon(0), dividend);
 111     }
 112   } else if ( is_power_of_2(d) ) {
 113     // division by +/- a power of 2
 114 
 115     // See if we can simply do a shift without rounding
 116     bool needs_rounding = true;
 117     const Type *dt = phase->type(dividend);
 118     const TypeInt *dti = dt->isa_int();
 119     if (dti && dti->_lo >= 0) {
 120       // we don't need to round a positive dividend
 121       needs_rounding = false;
 122     } else if( dividend->Opcode() == Op_AndI ) {
 123       // An AND mask of sufficient size clears the low bits and
 124       // I can avoid rounding.
 125       const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int();
 126       if( andconi_t && andconi_t->is_con() ) {
 127         jint andconi = andconi_t->get_con();
 128         if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) {
 129           if( (-andconi) == d ) // Remove AND if it clears bits which will be shifted
 130             dividend = dividend->in(1);
 131           needs_rounding = false;
 132         }
 133       }
 134     }
 135 
 136     // Add rounding to the shift to handle the sign bit
 137     int l = log2i_graceful(d - 1) + 1;
 138     if (needs_rounding) {
 139       // Divide-by-power-of-2 can be made into a shift, but you have to do
 140       // more math for the rounding.  You need to add 0 for positive
 141       // numbers, and "i-1" for negative numbers.  Example: i=4, so the
 142       // shift is by 2.  You need to add 3 to negative dividends and 0 to
 143       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
 144       // (-2+3)>>2 becomes 0, etc.
 145 
 146       // Compute 0 or -1, based on sign bit
 147       Node *sign = phase->transform(new RShiftINode(dividend, phase->intcon(N - 1)));
 148       // Mask sign bit to the low sign bits
 149       Node *round = phase->transform(new URShiftINode(sign, phase->intcon(N - l)));
 150       // Round up before shifting
 151       dividend = phase->transform(new AddINode(dividend, round));
 152     }
 153 
 154     // Shift for division
 155     q = new RShiftINode(dividend, phase->intcon(l));
 156 
 157     if (!d_pos) {
 158       q = new SubINode(phase->intcon(0), phase->transform(q));
 159     }
 160   } else {
 161     // Attempt the jint constant divide -> multiply transform found in
 162     //   "Division by Invariant Integers using Multiplication"
 163     //     by Granlund and Montgomery
 164     // See also "Hacker's Delight", chapter 10 by Warren.
 165 
 166     jint magic_const;
 167     jint shift_const;
 168     if (magic_int_divide_constants(d, magic_const, shift_const)) {
 169       Node *magic = phase->longcon(magic_const);
 170       Node *dividend_long = phase->transform(new ConvI2LNode(dividend));
 171 
 172       // Compute the high half of the dividend x magic multiplication
 173       Node *mul_hi = phase->transform(new MulLNode(dividend_long, magic));
 174 
 175       if (magic_const < 0) {
 176         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N)));
 177         mul_hi = phase->transform(new ConvL2INode(mul_hi));
 178 
 179         // The magic multiplier is too large for a 32 bit constant. We've adjusted
 180         // it down by 2^32, but have to add 1 dividend back in after the multiplication.
 181         // This handles the "overflow" case described by Granlund and Montgomery.
 182         mul_hi = phase->transform(new AddINode(dividend, mul_hi));
 183 
 184         // Shift over the (adjusted) mulhi
 185         if (shift_const != 0) {
 186           mul_hi = phase->transform(new RShiftINode(mul_hi, phase->intcon(shift_const)));
 187         }
 188       } else {
 189         // No add is required, we can merge the shifts together.
 190         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N + shift_const)));
 191         mul_hi = phase->transform(new ConvL2INode(mul_hi));
 192       }
 193 
 194       // Get a 0 or -1 from the sign of the dividend.
 195       Node *addend0 = mul_hi;
 196       Node *addend1 = phase->transform(new RShiftINode(dividend, phase->intcon(N-1)));
 197 
 198       // If the divisor is negative, swap the order of the input addends;
 199       // this has the effect of negating the quotient.
 200       if (!d_pos) {
 201         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 202       }
 203 
 204       // Adjust the final quotient by subtracting -1 (adding 1)
 205       // from the mul_hi.
 206       q = new SubINode(addend0, addend1);
 207     }
 208   }
 209 
 210   return q;
 211 }
 212 
 213 //---------------------magic_long_divide_constants-----------------------------
 214 // Compute magic multiplier and shift constant for converting a 64 bit divide
 215 // by constant into a multiply/shift/add series. Return false if calculations
 216 // fail.
 217 //
 218 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
 219 // minor type name and parameter changes.  Adjusted to 64 bit word width.
 220 static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) {
 221   int64_t p;
 222   uint64_t ad, anc, delta, q1, r1, q2, r2, t;
 223   const uint64_t two63 = UCONST64(0x8000000000000000);     // 2**63.
 224 
 225   ad = ABS(d);
 226   if (d == 0 || d == 1) return false;
 227   t = two63 + ((uint64_t)d >> 63);
 228   anc = t - 1 - t%ad;     // Absolute value of nc.
 229   p = 63;                 // Init. p.
 230   q1 = two63/anc;         // Init. q1 = 2**p/|nc|.
 231   r1 = two63 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
 232   q2 = two63/ad;          // Init. q2 = 2**p/|d|.
 233   r2 = two63 - q2*ad;     // Init. r2 = rem(2**p, |d|).
 234   do {
 235     p = p + 1;
 236     q1 = 2*q1;            // Update q1 = 2**p/|nc|.
 237     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
 238     if (r1 >= anc) {      // (Must be an unsigned
 239       q1 = q1 + 1;        // comparison here).
 240       r1 = r1 - anc;
 241     }
 242     q2 = 2*q2;            // Update q2 = 2**p/|d|.
 243     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
 244     if (r2 >= ad) {       // (Must be an unsigned
 245       q2 = q2 + 1;        // comparison here).
 246       r2 = r2 - ad;
 247     }
 248     delta = ad - r2;
 249   } while (q1 < delta || (q1 == delta && r1 == 0));
 250 
 251   M = q2 + 1;
 252   if (d < 0) M = -M;      // Magic number and
 253   s = p - 64;             // shift amount to return.
 254 
 255   return true;
 256 }
 257 
 258 //---------------------long_by_long_mulhi--------------------------------------
 259 // Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication
 260 static Node* long_by_long_mulhi(PhaseGVN* phase, Node* dividend, jlong magic_const) {
 261   // If the architecture supports a 64x64 mulhi, there is
 262   // no need to synthesize it in ideal nodes.
 263   if (Matcher::has_match_rule(Op_MulHiL)) {
 264     Node* v = phase->longcon(magic_const);
 265     return new MulHiLNode(dividend, v);
 266   }
 267 
 268   // Taken from Hacker's Delight, Fig. 8-2. Multiply high signed.
 269   // (http://www.hackersdelight.org/HDcode/mulhs.c)
 270   //
 271   // int mulhs(int u, int v) {
 272   //    unsigned u0, v0, w0;
 273   //    int u1, v1, w1, w2, t;
 274   //
 275   //    u0 = u & 0xFFFF;  u1 = u >> 16;
 276   //    v0 = v & 0xFFFF;  v1 = v >> 16;
 277   //    w0 = u0*v0;
 278   //    t  = u1*v0 + (w0 >> 16);
 279   //    w1 = t & 0xFFFF;
 280   //    w2 = t >> 16;
 281   //    w1 = u0*v1 + w1;
 282   //    return u1*v1 + w2 + (w1 >> 16);
 283   // }
 284   //
 285   // Note: The version above is for 32x32 multiplications, while the
 286   // following inline comments are adapted to 64x64.
 287 
 288   const int N = 64;
 289 
 290   // Dummy node to keep intermediate nodes alive during construction
 291   Node* hook = new Node(4);
 292 
 293   // u0 = u & 0xFFFFFFFF;  u1 = u >> 32;
 294   Node* u0 = phase->transform(new AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
 295   Node* u1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N / 2)));
 296   hook->init_req(0, u0);
 297   hook->init_req(1, u1);
 298 
 299   // v0 = v & 0xFFFFFFFF;  v1 = v >> 32;
 300   Node* v0 = phase->longcon(magic_const & 0xFFFFFFFF);
 301   Node* v1 = phase->longcon(magic_const >> (N / 2));
 302 
 303   // w0 = u0*v0;
 304   Node* w0 = phase->transform(new MulLNode(u0, v0));
 305 
 306   // t = u1*v0 + (w0 >> 32);
 307   Node* u1v0 = phase->transform(new MulLNode(u1, v0));
 308   Node* temp = phase->transform(new URShiftLNode(w0, phase->intcon(N / 2)));
 309   Node* t    = phase->transform(new AddLNode(u1v0, temp));
 310   hook->init_req(2, t);
 311 
 312   // w1 = t & 0xFFFFFFFF;
 313   Node* w1 = phase->transform(new AndLNode(t, phase->longcon(0xFFFFFFFF)));
 314   hook->init_req(3, w1);
 315 
 316   // w2 = t >> 32;
 317   Node* w2 = phase->transform(new RShiftLNode(t, phase->intcon(N / 2)));
 318 
 319   // w1 = u0*v1 + w1;
 320   Node* u0v1 = phase->transform(new MulLNode(u0, v1));
 321   w1         = phase->transform(new AddLNode(u0v1, w1));
 322 
 323   // return u1*v1 + w2 + (w1 >> 32);
 324   Node* u1v1  = phase->transform(new MulLNode(u1, v1));
 325   Node* temp1 = phase->transform(new AddLNode(u1v1, w2));
 326   Node* temp2 = phase->transform(new RShiftLNode(w1, phase->intcon(N / 2)));
 327 
 328   // Remove the bogus extra edges used to keep things alive
 329   hook->destruct(phase);
 330 
 331   return new AddLNode(temp1, temp2);
 332 }
 333 
 334 
 335 //--------------------------transform_long_divide------------------------------
 336 // Convert a division by constant divisor into an alternate Ideal graph.
 337 // Return NULL if no transformation occurs.
 338 static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {
 339   // Check for invalid divisors
 340   assert( divisor != 0L && divisor != min_jlong,
 341           "bad divisor for transforming to long multiply" );
 342 
 343   bool d_pos = divisor >= 0;
 344   jlong d = d_pos ? divisor : -divisor;
 345   const int N = 64;
 346 
 347   // Result
 348   Node *q = NULL;
 349 
 350   if (d == 1) {
 351     // division by +/- 1
 352     if (!d_pos) {
 353       // Just negate the value
 354       q = new SubLNode(phase->longcon(0), dividend);
 355     }
 356   } else if ( is_power_of_2(d) ) {
 357 
 358     // division by +/- a power of 2
 359 
 360     // See if we can simply do a shift without rounding
 361     bool needs_rounding = true;
 362     const Type *dt = phase->type(dividend);
 363     const TypeLong *dtl = dt->isa_long();
 364 
 365     if (dtl && dtl->_lo > 0) {
 366       // we don't need to round a positive dividend
 367       needs_rounding = false;
 368     } else if( dividend->Opcode() == Op_AndL ) {
 369       // An AND mask of sufficient size clears the low bits and
 370       // I can avoid rounding.
 371       const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();
 372       if( andconl_t && andconl_t->is_con() ) {
 373         jlong andconl = andconl_t->get_con();
 374         if( andconl < 0 && is_power_of_2(-andconl) && (-andconl) >= d ) {
 375           if( (-andconl) == d ) // Remove AND if it clears bits which will be shifted
 376             dividend = dividend->in(1);
 377           needs_rounding = false;
 378         }
 379       }
 380     }
 381 
 382     // Add rounding to the shift to handle the sign bit
 383     int l = log2i_graceful(d - 1) + 1;
 384     if (needs_rounding) {
 385       // Divide-by-power-of-2 can be made into a shift, but you have to do
 386       // more math for the rounding.  You need to add 0 for positive
 387       // numbers, and "i-1" for negative numbers.  Example: i=4, so the
 388       // shift is by 2.  You need to add 3 to negative dividends and 0 to
 389       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
 390       // (-2+3)>>2 becomes 0, etc.
 391 
 392       // Compute 0 or -1, based on sign bit
 393       Node *sign = phase->transform(new RShiftLNode(dividend, phase->intcon(N - 1)));
 394       // Mask sign bit to the low sign bits
 395       Node *round = phase->transform(new URShiftLNode(sign, phase->intcon(N - l)));
 396       // Round up before shifting
 397       dividend = phase->transform(new AddLNode(dividend, round));
 398     }
 399 
 400     // Shift for division
 401     q = new RShiftLNode(dividend, phase->intcon(l));
 402 
 403     if (!d_pos) {
 404       q = new SubLNode(phase->longcon(0), phase->transform(q));
 405     }
 406   } else if ( !Matcher::use_asm_for_ldiv_by_con(d) ) { // Use hardware DIV instruction when
 407                                                        // it is faster than code generated below.
 408     // Attempt the jlong constant divide -> multiply transform found in
 409     //   "Division by Invariant Integers using Multiplication"
 410     //     by Granlund and Montgomery
 411     // See also "Hacker's Delight", chapter 10 by Warren.
 412 
 413     jlong magic_const;
 414     jint shift_const;
 415     if (magic_long_divide_constants(d, magic_const, shift_const)) {
 416       // Compute the high half of the dividend x magic multiplication
 417       Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
 418 
 419       // The high half of the 128-bit multiply is computed.
 420       if (magic_const < 0) {
 421         // The magic multiplier is too large for a 64 bit constant. We've adjusted
 422         // it down by 2^64, but have to add 1 dividend back in after the multiplication.
 423         // This handles the "overflow" case described by Granlund and Montgomery.
 424         mul_hi = phase->transform(new AddLNode(dividend, mul_hi));
 425       }
 426 
 427       // Shift over the (adjusted) mulhi
 428       if (shift_const != 0) {
 429         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(shift_const)));
 430       }
 431 
 432       // Get a 0 or -1 from the sign of the dividend.
 433       Node *addend0 = mul_hi;
 434       Node *addend1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N-1)));
 435 
 436       // If the divisor is negative, swap the order of the input addends;
 437       // this has the effect of negating the quotient.
 438       if (!d_pos) {
 439         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 440       }
 441 
 442       // Adjust the final quotient by subtracting -1 (adding 1)
 443       // from the mul_hi.
 444       q = new SubLNode(addend0, addend1);
 445     }
 446   }
 447 
 448   return q;
 449 }
 450 
 451 //=============================================================================
 452 //------------------------------Identity---------------------------------------
 453 // If the divisor is 1, we are an identity on the dividend.
 454 Node* DivINode::Identity(PhaseGVN* phase) {
 455   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
 456 }
 457 
 458 //------------------------------Idealize---------------------------------------
 459 // Divides can be changed to multiplies and/or shifts
 460 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 461   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 462   // Don't bother trying to transform a dead node
 463   if( in(0) && in(0)->is_top() )  return NULL;
 464 
 465   const Type *t = phase->type( in(2) );
 466   if( t == TypeInt::ONE )       // Identity?
 467     return NULL;                // Skip it
 468 
 469   const TypeInt *ti = t->isa_int();
 470   if( !ti ) return NULL;
 471 
 472   // Check for useless control input
 473   // Check for excluding div-zero case
 474   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
 475     set_req(0, NULL);           // Yank control input
 476     return this;
 477   }
 478 
 479   if( !ti->is_con() ) return NULL;
 480   jint i = ti->get_con();       // Get divisor
 481 
 482   if (i == 0) return NULL;      // Dividing by zero constant does not idealize
 483 
 484   // Dividing by MININT does not optimize as a power-of-2 shift.
 485   if( i == min_jint ) return NULL;
 486 
 487   return transform_int_divide( phase, in(1), i );
 488 }
 489 
 490 //------------------------------Value------------------------------------------
 491 // A DivINode divides its inputs.  The third input is a Control input, used to
 492 // prevent hoisting the divide above an unsafe test.
 493 const Type* DivINode::Value(PhaseGVN* phase) const {
 494   // Either input is TOP ==> the result is TOP
 495   const Type *t1 = phase->type( in(1) );
 496   const Type *t2 = phase->type( in(2) );
 497   if( t1 == Type::TOP ) return Type::TOP;
 498   if( t2 == Type::TOP ) return Type::TOP;
 499 
 500   // x/x == 1 since we always generate the dynamic divisor check for 0.
 501   if (in(1) == in(2)) {
 502     return TypeInt::ONE;
 503   }
 504 
 505   // Either input is BOTTOM ==> the result is the local BOTTOM
 506   const Type *bot = bottom_type();
 507   if( (t1 == bot) || (t2 == bot) ||
 508       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 509     return bot;
 510 
 511   // Divide the two numbers.  We approximate.
 512   // If divisor is a constant and not zero
 513   const TypeInt *i1 = t1->is_int();
 514   const TypeInt *i2 = t2->is_int();
 515   int widen = MAX2(i1->_widen, i2->_widen);
 516 
 517   if( i2->is_con() && i2->get_con() != 0 ) {
 518     int32_t d = i2->get_con(); // Divisor
 519     jint lo, hi;
 520     if( d >= 0 ) {
 521       lo = i1->_lo/d;
 522       hi = i1->_hi/d;
 523     } else {
 524       if( d == -1 && i1->_lo == min_jint ) {
 525         // 'min_jint/-1' throws arithmetic exception during compilation
 526         lo = min_jint;
 527         // do not support holes, 'hi' must go to either min_jint or max_jint:
 528         // [min_jint, -10]/[-1,-1] ==> [min_jint] UNION [10,max_jint]
 529         hi = i1->_hi == min_jint ? min_jint : max_jint;
 530       } else {
 531         lo = i1->_hi/d;
 532         hi = i1->_lo/d;
 533       }
 534     }
 535     return TypeInt::make(lo, hi, widen);
 536   }
 537 
 538   // If the dividend is a constant
 539   if( i1->is_con() ) {
 540     int32_t d = i1->get_con();
 541     if( d < 0 ) {
 542       if( d == min_jint ) {
 543         //  (-min_jint) == min_jint == (min_jint / -1)
 544         return TypeInt::make(min_jint, max_jint/2 + 1, widen);
 545       } else {
 546         return TypeInt::make(d, -d, widen);
 547       }
 548     }
 549     return TypeInt::make(-d, d, widen);
 550   }
 551 
 552   // Otherwise we give up all hope
 553   return TypeInt::INT;
 554 }
 555 
 556 
 557 //=============================================================================
 558 //------------------------------Identity---------------------------------------
 559 // If the divisor is 1, we are an identity on the dividend.
 560 Node* DivLNode::Identity(PhaseGVN* phase) {
 561   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
 562 }
 563 
 564 //------------------------------Idealize---------------------------------------
 565 // Dividing by a power of 2 is a shift.
 566 Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) {
 567   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 568   // Don't bother trying to transform a dead node
 569   if( in(0) && in(0)->is_top() )  return NULL;
 570 
 571   const Type *t = phase->type( in(2) );
 572   if( t == TypeLong::ONE )      // Identity?
 573     return NULL;                // Skip it
 574 
 575   const TypeLong *tl = t->isa_long();
 576   if( !tl ) return NULL;
 577 
 578   // Check for useless control input
 579   // Check for excluding div-zero case
 580   if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
 581     set_req(0, NULL);           // Yank control input
 582     return this;
 583   }
 584 
 585   if( !tl->is_con() ) return NULL;
 586   jlong l = tl->get_con();      // Get divisor
 587 
 588   if (l == 0) return NULL;      // Dividing by zero constant does not idealize
 589 
 590   // Dividing by MINLONG does not optimize as a power-of-2 shift.
 591   if( l == min_jlong ) return NULL;
 592 
 593   return transform_long_divide( phase, in(1), l );
 594 }
 595 
 596 //------------------------------Value------------------------------------------
 597 // A DivLNode divides its inputs.  The third input is a Control input, used to
 598 // prevent hoisting the divide above an unsafe test.
 599 const Type* DivLNode::Value(PhaseGVN* phase) const {
 600   // Either input is TOP ==> the result is TOP
 601   const Type *t1 = phase->type( in(1) );
 602   const Type *t2 = phase->type( in(2) );
 603   if( t1 == Type::TOP ) return Type::TOP;
 604   if( t2 == Type::TOP ) return Type::TOP;
 605 
 606   // x/x == 1 since we always generate the dynamic divisor check for 0.
 607   if (in(1) == in(2)) {
 608     return TypeLong::ONE;
 609   }
 610 
 611   // Either input is BOTTOM ==> the result is the local BOTTOM
 612   const Type *bot = bottom_type();
 613   if( (t1 == bot) || (t2 == bot) ||
 614       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 615     return bot;
 616 
 617   // Divide the two numbers.  We approximate.
 618   // If divisor is a constant and not zero
 619   const TypeLong *i1 = t1->is_long();
 620   const TypeLong *i2 = t2->is_long();
 621   int widen = MAX2(i1->_widen, i2->_widen);
 622 
 623   if( i2->is_con() && i2->get_con() != 0 ) {
 624     jlong d = i2->get_con();    // Divisor
 625     jlong lo, hi;
 626     if( d >= 0 ) {
 627       lo = i1->_lo/d;
 628       hi = i1->_hi/d;
 629     } else {
 630       if( d == CONST64(-1) && i1->_lo == min_jlong ) {
 631         // 'min_jlong/-1' throws arithmetic exception during compilation
 632         lo = min_jlong;
 633         // do not support holes, 'hi' must go to either min_jlong or max_jlong:
 634         // [min_jlong, -10]/[-1,-1] ==> [min_jlong] UNION [10,max_jlong]
 635         hi = i1->_hi == min_jlong ? min_jlong : max_jlong;
 636       } else {
 637         lo = i1->_hi/d;
 638         hi = i1->_lo/d;
 639       }
 640     }
 641     return TypeLong::make(lo, hi, widen);
 642   }
 643 
 644   // If the dividend is a constant
 645   if( i1->is_con() ) {
 646     jlong d = i1->get_con();
 647     if( d < 0 ) {
 648       if( d == min_jlong ) {
 649         //  (-min_jlong) == min_jlong == (min_jlong / -1)
 650         return TypeLong::make(min_jlong, max_jlong/2 + 1, widen);
 651       } else {
 652         return TypeLong::make(d, -d, widen);
 653       }
 654     }
 655     return TypeLong::make(-d, d, widen);
 656   }
 657 
 658   // Otherwise we give up all hope
 659   return TypeLong::LONG;
 660 }
 661 
 662 
 663 //=============================================================================
 664 //------------------------------Value------------------------------------------
 665 // An DivFNode divides its inputs.  The third input is a Control input, used to
 666 // prevent hoisting the divide above an unsafe test.
 667 const Type* DivFNode::Value(PhaseGVN* phase) const {
 668   // Either input is TOP ==> the result is TOP
 669   const Type *t1 = phase->type( in(1) );
 670   const Type *t2 = phase->type( in(2) );
 671   if( t1 == Type::TOP ) return Type::TOP;
 672   if( t2 == Type::TOP ) return Type::TOP;
 673 
 674   // Either input is BOTTOM ==> the result is the local BOTTOM
 675   const Type *bot = bottom_type();
 676   if( (t1 == bot) || (t2 == bot) ||
 677       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 678     return bot;
 679 
 680   // x/x == 1, we ignore 0/0.
 681   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 682   // Does not work for variables because of NaN's
 683   if (in(1) == in(2) && t1->base() == Type::FloatCon &&
 684       !g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) { // could be negative ZERO or NaN
 685     return TypeF::ONE;
 686   }
 687 
 688   if( t2 == TypeF::ONE )
 689     return t1;
 690 
 691   // If divisor is a constant and not zero, divide them numbers
 692   if( t1->base() == Type::FloatCon &&
 693       t2->base() == Type::FloatCon &&
 694       t2->getf() != 0.0 ) // could be negative zero
 695     return TypeF::make( t1->getf()/t2->getf() );
 696 
 697   // If the dividend is a constant zero
 698   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 699   // Test TypeF::ZERO is not sufficient as it could be negative zero
 700 
 701   if( t1 == TypeF::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0 )
 702     return TypeF::ZERO;
 703 
 704   // Otherwise we give up all hope
 705   return Type::FLOAT;
 706 }
 707 
 708 //------------------------------isA_Copy---------------------------------------
 709 // Dividing by self is 1.
 710 // If the divisor is 1, we are an identity on the dividend.
 711 Node* DivFNode::Identity(PhaseGVN* phase) {
 712   return (phase->type( in(2) ) == TypeF::ONE) ? in(1) : this;
 713 }
 714 
 715 
 716 //------------------------------Idealize---------------------------------------
 717 Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 718   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 719   // Don't bother trying to transform a dead node
 720   if( in(0) && in(0)->is_top() )  return NULL;
 721 
 722   const Type *t2 = phase->type( in(2) );
 723   if( t2 == TypeF::ONE )         // Identity?
 724     return NULL;                // Skip it
 725 
 726   const TypeF *tf = t2->isa_float_constant();
 727   if( !tf ) return NULL;
 728   if( tf->base() != Type::FloatCon ) return NULL;
 729 
 730   // Check for out of range values
 731   if( tf->is_nan() || !tf->is_finite() ) return NULL;
 732 
 733   // Get the value
 734   float f = tf->getf();
 735   int exp;
 736 
 737   // Only for special case of dividing by a power of 2
 738   if( frexp((double)f, &exp) != 0.5 ) return NULL;
 739 
 740   // Limit the range of acceptable exponents
 741   if( exp < -126 || exp > 126 ) return NULL;
 742 
 743   // Compute the reciprocal
 744   float reciprocal = ((float)1.0) / f;
 745 
 746   assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 747 
 748   // return multiplication by the reciprocal
 749   return (new MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
 750 }
 751 
 752 //=============================================================================
 753 //------------------------------Value------------------------------------------
 754 // An DivDNode divides its inputs.  The third input is a Control input, used to
 755 // prevent hoisting the divide above an unsafe test.
 756 const Type* DivDNode::Value(PhaseGVN* phase) const {
 757   // Either input is TOP ==> the result is TOP
 758   const Type *t1 = phase->type( in(1) );
 759   const Type *t2 = phase->type( in(2) );
 760   if( t1 == Type::TOP ) return Type::TOP;
 761   if( t2 == Type::TOP ) return Type::TOP;
 762 
 763   // Either input is BOTTOM ==> the result is the local BOTTOM
 764   const Type *bot = bottom_type();
 765   if( (t1 == bot) || (t2 == bot) ||
 766       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 767     return bot;
 768 
 769   // x/x == 1, we ignore 0/0.
 770   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 771   // Does not work for variables because of NaN's
 772   if (in(1) == in(2) && t1->base() == Type::DoubleCon &&
 773       !g_isnan(t1->getd()) && g_isfinite(t1->getd()) && t1->getd() != 0.0) { // could be negative ZERO or NaN
 774     return TypeD::ONE;
 775   }
 776 
 777   if( t2 == TypeD::ONE )
 778     return t1;
 779 
 780   // IA32 would only execute this for non-strict FP, which is never the
 781   // case now.
 782 #if ! defined(IA32)
 783   // If divisor is a constant and not zero, divide them numbers
 784   if( t1->base() == Type::DoubleCon &&
 785       t2->base() == Type::DoubleCon &&
 786       t2->getd() != 0.0 ) // could be negative zero
 787     return TypeD::make( t1->getd()/t2->getd() );
 788 #endif
 789 
 790   // If the dividend is a constant zero
 791   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 792   // Test TypeF::ZERO is not sufficient as it could be negative zero
 793   if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )
 794     return TypeD::ZERO;
 795 
 796   // Otherwise we give up all hope
 797   return Type::DOUBLE;
 798 }
 799 
 800 
 801 //------------------------------isA_Copy---------------------------------------
 802 // Dividing by self is 1.
 803 // If the divisor is 1, we are an identity on the dividend.
 804 Node* DivDNode::Identity(PhaseGVN* phase) {
 805   return (phase->type( in(2) ) == TypeD::ONE) ? in(1) : this;
 806 }
 807 
 808 //------------------------------Idealize---------------------------------------
 809 Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 810   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 811   // Don't bother trying to transform a dead node
 812   if( in(0) && in(0)->is_top() )  return NULL;
 813 
 814   const Type *t2 = phase->type( in(2) );
 815   if( t2 == TypeD::ONE )         // Identity?
 816     return NULL;                // Skip it
 817 
 818   const TypeD *td = t2->isa_double_constant();
 819   if( !td ) return NULL;
 820   if( td->base() != Type::DoubleCon ) return NULL;
 821 
 822   // Check for out of range values
 823   if( td->is_nan() || !td->is_finite() ) return NULL;
 824 
 825   // Get the value
 826   double d = td->getd();
 827   int exp;
 828 
 829   // Only for special case of dividing by a power of 2
 830   if( frexp(d, &exp) != 0.5 ) return NULL;
 831 
 832   // Limit the range of acceptable exponents
 833   if( exp < -1021 || exp > 1022 ) return NULL;
 834 
 835   // Compute the reciprocal
 836   double reciprocal = 1.0 / d;
 837 
 838   assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 839 
 840   // return multiplication by the reciprocal
 841   return (new MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
 842 }
 843 
 844 //=============================================================================
 845 //------------------------------Idealize---------------------------------------
 846 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 847   // Check for dead control input
 848   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
 849   // Don't bother trying to transform a dead node
 850   if( in(0) && in(0)->is_top() )  return NULL;
 851 
 852   // Get the modulus
 853   const Type *t = phase->type( in(2) );
 854   if( t == Type::TOP ) return NULL;
 855   const TypeInt *ti = t->is_int();
 856 
 857   // Check for useless control input
 858   // Check for excluding mod-zero case
 859   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
 860     set_req(0, NULL);        // Yank control input
 861     return this;
 862   }
 863 
 864   // See if we are MOD'ing by 2^k or 2^k-1.
 865   if( !ti->is_con() ) return NULL;
 866   jint con = ti->get_con();
 867 
 868   Node *hook = new Node(1);
 869 
 870   // First, special check for modulo 2^k-1
 871   if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
 872     uint k = exact_log2(con+1);  // Extract k
 873 
 874     // Basic algorithm by David Detlefs.  See fastmod_int.java for gory details.
 875     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*/};
 876     int trip_count = 1;
 877     if( k < ARRAY_SIZE(unroll_factor))  trip_count = unroll_factor[k];
 878 
 879     // If the unroll factor is not too large, and if conditional moves are
 880     // ok, then use this case
 881     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
 882       Node *x = in(1);            // Value being mod'd
 883       Node *divisor = in(2);      // Also is mask
 884 
 885       hook->init_req(0, x);       // Add a use to x to prevent him from dying
 886       // Generate code to reduce X rapidly to nearly 2^k-1.
 887       for( int i = 0; i < trip_count; i++ ) {
 888         Node *xl = phase->transform( new AndINode(x,divisor) );
 889         Node *xh = phase->transform( new RShiftINode(x,phase->intcon(k)) ); // Must be signed
 890         x = phase->transform( new AddINode(xh,xl) );
 891         hook->set_req(0, x);
 892       }
 893 
 894       // Generate sign-fixup code.  Was original value positive?
 895       // int hack_res = (i >= 0) ? divisor : 1;
 896       Node *cmp1 = phase->transform( new CmpINode( in(1), phase->intcon(0) ) );
 897       Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
 898       Node *cmov1= phase->transform( new CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
 899       // if( x >= hack_res ) x -= divisor;
 900       Node *sub  = phase->transform( new SubINode( x, divisor ) );
 901       Node *cmp2 = phase->transform( new CmpINode( x, cmov1 ) );
 902       Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
 903       // Convention is to not transform the return value of an Ideal
 904       // since Ideal is expected to return a modified 'this' or a new node.
 905       Node *cmov2= new CMoveINode(bol2, x, sub, TypeInt::INT);
 906       // cmov2 is now the mod
 907 
 908       // Now remove the bogus extra edges used to keep things alive
 909       hook->destruct(phase);
 910       return cmov2;
 911     }
 912   }
 913 
 914   // Fell thru, the unroll case is not appropriate. Transform the modulo
 915   // into a long multiply/int multiply/subtract case
 916 
 917   // Cannot handle mod 0, and min_jint isn't handled by the transform
 918   if( con == 0 || con == min_jint ) return NULL;
 919 
 920   // Get the absolute value of the constant; at this point, we can use this
 921   jint pos_con = (con >= 0) ? con : -con;
 922 
 923   // integer Mod 1 is always 0
 924   if( pos_con == 1 ) return new ConINode(TypeInt::ZERO);
 925 
 926   int log2_con = -1;
 927 
 928   // If this is a power of two, they maybe we can mask it
 929   if (is_power_of_2(pos_con)) {
 930     log2_con = log2i_exact(pos_con);
 931 
 932     const Type *dt = phase->type(in(1));
 933     const TypeInt *dti = dt->isa_int();
 934 
 935     // See if this can be masked, if the dividend is non-negative
 936     if( dti && dti->_lo >= 0 )
 937       return ( new AndINode( in(1), phase->intcon( pos_con-1 ) ) );
 938   }
 939 
 940   // Save in(1) so that it cannot be changed or deleted
 941   hook->init_req(0, in(1));
 942 
 943   // Divide using the transform from DivI to MulL
 944   Node *result = transform_int_divide( phase, in(1), pos_con );
 945   if (result != NULL) {
 946     Node *divide = phase->transform(result);
 947 
 948     // Re-multiply, using a shift if this is a power of two
 949     Node *mult = NULL;
 950 
 951     if( log2_con >= 0 )
 952       mult = phase->transform( new LShiftINode( divide, phase->intcon( log2_con ) ) );
 953     else
 954       mult = phase->transform( new MulINode( divide, phase->intcon( pos_con ) ) );
 955 
 956     // Finally, subtract the multiplied divided value from the original
 957     result = new SubINode( in(1), mult );
 958   }
 959 
 960   // Now remove the bogus extra edges used to keep things alive
 961   hook->destruct(phase);
 962 
 963   // return the value
 964   return result;
 965 }
 966 
 967 //------------------------------Value------------------------------------------
 968 const Type* ModINode::Value(PhaseGVN* phase) const {
 969   // Either input is TOP ==> the result is TOP
 970   const Type *t1 = phase->type( in(1) );
 971   const Type *t2 = phase->type( in(2) );
 972   if( t1 == Type::TOP ) return Type::TOP;
 973   if( t2 == Type::TOP ) return Type::TOP;
 974 
 975   // We always generate the dynamic check for 0.
 976   // 0 MOD X is 0
 977   if( t1 == TypeInt::ZERO ) return TypeInt::ZERO;
 978   // X MOD X is 0
 979   if (in(1) == in(2)) {
 980     return TypeInt::ZERO;
 981   }
 982 
 983   // Either input is BOTTOM ==> the result is the local BOTTOM
 984   const Type *bot = bottom_type();
 985   if( (t1 == bot) || (t2 == bot) ||
 986       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 987     return bot;
 988 
 989   const TypeInt *i1 = t1->is_int();
 990   const TypeInt *i2 = t2->is_int();
 991   if( !i1->is_con() || !i2->is_con() ) {
 992     if( i1->_lo >= 0 && i2->_lo >= 0 )
 993       return TypeInt::POS;
 994     // If both numbers are not constants, we know little.
 995     return TypeInt::INT;
 996   }
 997   // Mod by zero?  Throw exception at runtime!
 998   if( !i2->get_con() ) return TypeInt::POS;
 999 
1000   // We must be modulo'ing 2 float constants.
1001   // Check for min_jint % '-1', result is defined to be '0'.
1002   if( i1->get_con() == min_jint && i2->get_con() == -1 )
1003     return TypeInt::ZERO;
1004 
1005   return TypeInt::make( i1->get_con() % i2->get_con() );
1006 }
1007 
1008 
1009 //=============================================================================
1010 //------------------------------Idealize---------------------------------------
1011 Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1012   // Check for dead control input
1013   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
1014   // Don't bother trying to transform a dead node
1015   if( in(0) && in(0)->is_top() )  return NULL;
1016 
1017   // Get the modulus
1018   const Type *t = phase->type( in(2) );
1019   if( t == Type::TOP ) return NULL;
1020   const TypeLong *tl = t->is_long();
1021 
1022   // Check for useless control input
1023   // Check for excluding mod-zero case
1024   if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
1025     set_req(0, NULL);        // Yank control input
1026     return this;
1027   }
1028 
1029   // See if we are MOD'ing by 2^k or 2^k-1.
1030   if( !tl->is_con() ) return NULL;
1031   jlong con = tl->get_con();
1032 
1033   Node *hook = new Node(1);
1034 
1035   // Expand mod
1036   if(con >= 0 && con < max_jlong && is_power_of_2(con + 1)) {
1037     uint k = log2i_exact(con + 1);  // Extract k
1038 
1039     // Basic algorithm by David Detlefs.  See fastmod_long.java for gory details.
1040     // Used to help a popular random number generator which does a long-mod
1041     // of 2^31-1 and shows up in SpecJBB and SciMark.
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*/};
1043     int trip_count = 1;
1044     if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
1045 
1046     // If the unroll factor is not too large, and if conditional moves are
1047     // ok, then use this case
1048     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1049       Node *x = in(1);            // Value being mod'd
1050       Node *divisor = in(2);      // Also is mask
1051 
1052       hook->init_req(0, x);       // Add a use to x to prevent him from dying
1053       // Generate code to reduce X rapidly to nearly 2^k-1.
1054       for( int i = 0; i < trip_count; i++ ) {
1055         Node *xl = phase->transform( new AndLNode(x,divisor) );
1056         Node *xh = phase->transform( new RShiftLNode(x,phase->intcon(k)) ); // Must be signed
1057         x = phase->transform( new AddLNode(xh,xl) );
1058         hook->set_req(0, x);    // Add a use to x to prevent him from dying
1059       }
1060 
1061       // Generate sign-fixup code.  Was original value positive?
1062       // long hack_res = (i >= 0) ? divisor : CONST64(1);
1063       Node *cmp1 = phase->transform( new CmpLNode( in(1), phase->longcon(0) ) );
1064       Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
1065       Node *cmov1= phase->transform( new CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
1066       // if( x >= hack_res ) x -= divisor;
1067       Node *sub  = phase->transform( new SubLNode( x, divisor ) );
1068       Node *cmp2 = phase->transform( new CmpLNode( x, cmov1 ) );
1069       Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
1070       // Convention is to not transform the return value of an Ideal
1071       // since Ideal is expected to return a modified 'this' or a new node.
1072       Node *cmov2= new CMoveLNode(bol2, x, sub, TypeLong::LONG);
1073       // cmov2 is now the mod
1074 
1075       // Now remove the bogus extra edges used to keep things alive
1076       hook->destruct(phase);
1077       return cmov2;
1078     }
1079   }
1080 
1081   // Fell thru, the unroll case is not appropriate. Transform the modulo
1082   // into a long multiply/int multiply/subtract case
1083 
1084   // Cannot handle mod 0, and min_jlong isn't handled by the transform
1085   if( con == 0 || con == min_jlong ) return NULL;
1086 
1087   // Get the absolute value of the constant; at this point, we can use this
1088   jlong pos_con = (con >= 0) ? con : -con;
1089 
1090   // integer Mod 1 is always 0
1091   if( pos_con == 1 ) return new ConLNode(TypeLong::ZERO);
1092 
1093   int log2_con = -1;
1094 
1095   // If this is a power of two, then maybe we can mask it
1096   if (is_power_of_2(pos_con)) {
1097     log2_con = log2i_exact(pos_con);
1098 
1099     const Type *dt = phase->type(in(1));
1100     const TypeLong *dtl = dt->isa_long();
1101 
1102     // See if this can be masked, if the dividend is non-negative
1103     if( dtl && dtl->_lo >= 0 )
1104       return ( new AndLNode( in(1), phase->longcon( pos_con-1 ) ) );
1105   }
1106 
1107   // Save in(1) so that it cannot be changed or deleted
1108   hook->init_req(0, in(1));
1109 
1110   // Divide using the transform from DivL to MulL
1111   Node *result = transform_long_divide( phase, in(1), pos_con );
1112   if (result != NULL) {
1113     Node *divide = phase->transform(result);
1114 
1115     // Re-multiply, using a shift if this is a power of two
1116     Node *mult = NULL;
1117 
1118     if( log2_con >= 0 )
1119       mult = phase->transform( new LShiftLNode( divide, phase->intcon( log2_con ) ) );
1120     else
1121       mult = phase->transform( new MulLNode( divide, phase->longcon( pos_con ) ) );
1122 
1123     // Finally, subtract the multiplied divided value from the original
1124     result = new SubLNode( in(1), mult );
1125   }
1126 
1127   // Now remove the bogus extra edges used to keep things alive
1128   hook->destruct(phase);
1129 
1130   // return the value
1131   return result;
1132 }
1133 
1134 //------------------------------Value------------------------------------------
1135 const Type* ModLNode::Value(PhaseGVN* phase) const {
1136   // Either input is TOP ==> the result is TOP
1137   const Type *t1 = phase->type( in(1) );
1138   const Type *t2 = phase->type( in(2) );
1139   if( t1 == Type::TOP ) return Type::TOP;
1140   if( t2 == Type::TOP ) return Type::TOP;
1141 
1142   // We always generate the dynamic check for 0.
1143   // 0 MOD X is 0
1144   if( t1 == TypeLong::ZERO ) return TypeLong::ZERO;
1145   // X MOD X is 0
1146   if (in(1) == in(2)) {
1147     return TypeLong::ZERO;
1148   }
1149 
1150   // Either input is BOTTOM ==> the result is the local BOTTOM
1151   const Type *bot = bottom_type();
1152   if( (t1 == bot) || (t2 == bot) ||
1153       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1154     return bot;
1155 
1156   const TypeLong *i1 = t1->is_long();
1157   const TypeLong *i2 = t2->is_long();
1158   if( !i1->is_con() || !i2->is_con() ) {
1159     if( i1->_lo >= CONST64(0) && i2->_lo >= CONST64(0) )
1160       return TypeLong::POS;
1161     // If both numbers are not constants, we know little.
1162     return TypeLong::LONG;
1163   }
1164   // Mod by zero?  Throw exception at runtime!
1165   if( !i2->get_con() ) return TypeLong::POS;
1166 
1167   // We must be modulo'ing 2 float constants.
1168   // Check for min_jint % '-1', result is defined to be '0'.
1169   if( i1->get_con() == min_jlong && i2->get_con() == -1 )
1170     return TypeLong::ZERO;
1171 
1172   return TypeLong::make( i1->get_con() % i2->get_con() );
1173 }
1174 
1175 
1176 //=============================================================================
1177 //------------------------------Value------------------------------------------
1178 const Type* ModFNode::Value(PhaseGVN* phase) const {
1179   // Either input is TOP ==> the result is TOP
1180   const Type *t1 = phase->type( in(1) );
1181   const Type *t2 = phase->type( in(2) );
1182   if( t1 == Type::TOP ) return Type::TOP;
1183   if( t2 == Type::TOP ) return Type::TOP;
1184 
1185   // Either input is BOTTOM ==> the result is the local BOTTOM
1186   const Type *bot = bottom_type();
1187   if( (t1 == bot) || (t2 == bot) ||
1188       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1189     return bot;
1190 
1191   // If either number is not a constant, we know nothing.
1192   if ((t1->base() != Type::FloatCon) || (t2->base() != Type::FloatCon)) {
1193     return Type::FLOAT;         // note: x%x can be either NaN or 0
1194   }
1195 
1196   float f1 = t1->getf();
1197   float f2 = t2->getf();
1198   jint  x1 = jint_cast(f1);     // note:  *(int*)&f1, not just (int)f1
1199   jint  x2 = jint_cast(f2);
1200 
1201   // If either is a NaN, return an input NaN
1202   if (g_isnan(f1))    return t1;
1203   if (g_isnan(f2))    return t2;
1204 
1205   // If an operand is infinity or the divisor is +/- zero, punt.
1206   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jint)
1207     return Type::FLOAT;
1208 
1209   // We must be modulo'ing 2 float constants.
1210   // Make sure that the sign of the fmod is equal to the sign of the dividend
1211   jint xr = jint_cast(fmod(f1, f2));
1212   if ((x1 ^ xr) < 0) {
1213     xr ^= min_jint;
1214   }
1215 
1216   return TypeF::make(jfloat_cast(xr));
1217 }
1218 
1219 
1220 //=============================================================================
1221 //------------------------------Value------------------------------------------
1222 const Type* ModDNode::Value(PhaseGVN* phase) const {
1223   // Either input is TOP ==> the result is TOP
1224   const Type *t1 = phase->type( in(1) );
1225   const Type *t2 = phase->type( in(2) );
1226   if( t1 == Type::TOP ) return Type::TOP;
1227   if( t2 == Type::TOP ) return Type::TOP;
1228 
1229   // Either input is BOTTOM ==> the result is the local BOTTOM
1230   const Type *bot = bottom_type();
1231   if( (t1 == bot) || (t2 == bot) ||
1232       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1233     return bot;
1234 
1235   // If either number is not a constant, we know nothing.
1236   if ((t1->base() != Type::DoubleCon) || (t2->base() != Type::DoubleCon)) {
1237     return Type::DOUBLE;        // note: x%x can be either NaN or 0
1238   }
1239 
1240   double f1 = t1->getd();
1241   double f2 = t2->getd();
1242   jlong  x1 = jlong_cast(f1);   // note:  *(long*)&f1, not just (long)f1
1243   jlong  x2 = jlong_cast(f2);
1244 
1245   // If either is a NaN, return an input NaN
1246   if (g_isnan(f1))    return t1;
1247   if (g_isnan(f2))    return t2;
1248 
1249   // If an operand is infinity or the divisor is +/- zero, punt.
1250   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jlong)
1251     return Type::DOUBLE;
1252 
1253   // We must be modulo'ing 2 double constants.
1254   // Make sure that the sign of the fmod is equal to the sign of the dividend
1255   jlong xr = jlong_cast(fmod(f1, f2));
1256   if ((x1 ^ xr) < 0) {
1257     xr ^= min_jlong;
1258   }
1259 
1260   return TypeD::make(jdouble_cast(xr));
1261 }
1262 
1263 //=============================================================================
1264 
1265 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
1266   init_req(0, c);
1267   init_req(1, dividend);
1268   init_req(2, divisor);
1269 }
1270 
1271 //------------------------------make------------------------------------------
1272 DivModINode* DivModINode::make(Node* div_or_mod) {
1273   Node* n = div_or_mod;
1274   assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
1275          "only div or mod input pattern accepted");
1276 
1277   DivModINode* divmod = new DivModINode(n->in(0), n->in(1), n->in(2));
1278   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1279   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1280   return divmod;
1281 }
1282 
1283 //------------------------------make------------------------------------------
1284 DivModLNode* DivModLNode::make(Node* div_or_mod) {
1285   Node* n = div_or_mod;
1286   assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
1287          "only div or mod input pattern accepted");
1288 
1289   DivModLNode* divmod = new DivModLNode(n->in(0), n->in(1), n->in(2));
1290   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1291   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1292   return divmod;
1293 }
1294 
1295 //------------------------------match------------------------------------------
1296 // return result(s) along with their RegMask info
1297 Node *DivModINode::match(const ProjNode *proj, const Matcher *match, const RegMask* mask) {
1298   uint ideal_reg = proj->ideal_reg();
1299   RegMask rm;
1300   if (proj->_con == div_proj_num) {
1301     rm = match->divI_proj_mask();
1302   } else {
1303     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1304     rm = match->modI_proj_mask();
1305   }
1306   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1307 }
1308 
1309 
1310 //------------------------------match------------------------------------------
1311 // return result(s) along with their RegMask info
1312 Node *DivModLNode::match(const ProjNode *proj, const Matcher *match, const RegMask* mask) {
1313   uint ideal_reg = proj->ideal_reg();
1314   RegMask rm;
1315   if (proj->_con == div_proj_num) {
1316     rm = match->divL_proj_mask();
1317   } else {
1318     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1319     rm = match->modL_proj_mask();
1320   }
1321   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1322 }