1 /*
   2  * Copyright 1997-2008 Sun Microsystems, Inc.  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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
  20  * CA 95054 USA or visit www.sun.com if you need additional information or
  21  * have any questions.
  22  *
  23  */
  24 
  25 // Portions of code courtesy of Clifford Click
  26 
  27 // Optimization - Graph Style
  28 
  29 #include "incls/_precompiled.incl"
  30 #include "incls/_divnode.cpp.incl"
  31 #include <math.h>
  32 
  33 //----------------------magic_int_divide_constants-----------------------------
  34 // Compute magic multiplier and shift constant for converting a 32 bit divide
  35 // by constant into a multiply/shift/add series. Return false if calculations
  36 // fail.
  37 //
  38 // Borrowed almost verbatum from Hacker's Delight by Henry S. Warren, Jr. with
  39 // minor type name and parameter changes.
  40 static bool magic_int_divide_constants(jint d, jint &M, jint &s) {
  41   int32_t p;
  42   uint32_t ad, anc, delta, q1, r1, q2, r2, t;
  43   const uint32_t two31 = 0x80000000L;     // 2**31.
  44 
  45   ad = ABS(d);
  46   if (d == 0 || d == 1) return false;
  47   t = two31 + ((uint32_t)d >> 31);
  48   anc = t - 1 - t%ad;     // Absolute value of nc.
  49   p = 31;                 // Init. p.
  50   q1 = two31/anc;         // Init. q1 = 2**p/|nc|.
  51   r1 = two31 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
  52   q2 = two31/ad;          // Init. q2 = 2**p/|d|.
  53   r2 = two31 - q2*ad;     // Init. r2 = rem(2**p, |d|).
  54   do {
  55     p = p + 1;
  56     q1 = 2*q1;            // Update q1 = 2**p/|nc|.
  57     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
  58     if (r1 >= anc) {      // (Must be an unsigned
  59       q1 = q1 + 1;        // comparison here).
  60       r1 = r1 - anc;
  61     }
  62     q2 = 2*q2;            // Update q2 = 2**p/|d|.
  63     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
  64     if (r2 >= ad) {       // (Must be an unsigned
  65       q2 = q2 + 1;        // comparison here).
  66       r2 = r2 - ad;
  67     }
  68     delta = ad - r2;
  69   } while (q1 < delta || (q1 == delta && r1 == 0));
  70 
  71   M = q2 + 1;
  72   if (d < 0) M = -M;      // Magic number and
  73   s = p - 32;             // shift amount to return.
  74 
  75   return true;
  76 }
  77 
  78 //--------------------------transform_int_divide-------------------------------
  79 // Convert a division by constant divisor into an alternate Ideal graph.
  80 // Return NULL if no transformation occurs.
  81 static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) {
  82 
  83   // Check for invalid divisors
  84   assert( divisor != 0 && divisor != min_jint,
  85           "bad divisor for transforming to long multiply" );
  86 
  87   bool d_pos = divisor >= 0;
  88   jint d = d_pos ? divisor : -divisor;
  89   const int N = 32;
  90 
  91   // Result
  92   Node *q = NULL;
  93 
  94   if (d == 1) {
  95     // division by +/- 1
  96     if (!d_pos) {
  97       // Just negate the value
  98       q = new (phase->C, 3) SubINode(phase->intcon(0), dividend);
  99     }
 100   } else if ( is_power_of_2(d) ) {
 101     // division by +/- a power of 2
 102 
 103     // See if we can simply do a shift without rounding
 104     bool needs_rounding = true;
 105     const Type *dt = phase->type(dividend);
 106     const TypeInt *dti = dt->isa_int();
 107     if (dti && dti->_lo >= 0) {
 108       // we don't need to round a positive dividend
 109       needs_rounding = false;
 110     } else if( dividend->Opcode() == Op_AndI ) {
 111       // An AND mask of sufficient size clears the low bits and
 112       // I can avoid rounding.
 113       const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int();
 114       if( andconi_t && andconi_t->is_con() ) {
 115         jint andconi = andconi_t->get_con();
 116         if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) {
 117           dividend = dividend->in(1);
 118           needs_rounding = false;
 119         }
 120       }
 121     }
 122 
 123     // Add rounding to the shift to handle the sign bit
 124     int l = log2_intptr(d-1)+1;
 125     if (needs_rounding) {
 126       // Divide-by-power-of-2 can be made into a shift, but you have to do
 127       // more math for the rounding.  You need to add 0 for positive
 128       // numbers, and "i-1" for negative numbers.  Example: i=4, so the
 129       // shift is by 2.  You need to add 3 to negative dividends and 0 to
 130       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
 131       // (-2+3)>>2 becomes 0, etc.
 132 
 133       // Compute 0 or -1, based on sign bit
 134       Node *sign = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N - 1)));
 135       // Mask sign bit to the low sign bits
 136       Node *round = phase->transform(new (phase->C, 3) URShiftINode(sign, phase->intcon(N - l)));
 137       // Round up before shifting
 138       dividend = phase->transform(new (phase->C, 3) AddINode(dividend, round));
 139     }
 140 
 141     // Shift for division
 142     q = new (phase->C, 3) RShiftINode(dividend, phase->intcon(l));
 143 
 144     if (!d_pos) {
 145       q = new (phase->C, 3) SubINode(phase->intcon(0), phase->transform(q));
 146     }
 147   } else {
 148     // Attempt the jint constant divide -> multiply transform found in
 149     //   "Division by Invariant Integers using Multiplication"
 150     //     by Granlund and Montgomery
 151     // See also "Hacker's Delight", chapter 10 by Warren.
 152 
 153     jint magic_const;
 154     jint shift_const;
 155     if (magic_int_divide_constants(d, magic_const, shift_const)) {
 156       Node *magic = phase->longcon(magic_const);
 157       Node *dividend_long = phase->transform(new (phase->C, 2) ConvI2LNode(dividend));
 158 
 159       // Compute the high half of the dividend x magic multiplication
 160       Node *mul_hi = phase->transform(new (phase->C, 3) MulLNode(dividend_long, magic));
 161 
 162       if (magic_const < 0) {
 163         mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(N)));
 164         mul_hi = phase->transform(new (phase->C, 2) ConvL2INode(mul_hi));
 165 
 166         // The magic multiplier is too large for a 32 bit constant. We've adjusted
 167         // it down by 2^32, but have to add 1 dividend back in after the multiplication.
 168         // This handles the "overflow" case described by Granlund and Montgomery.
 169         mul_hi = phase->transform(new (phase->C, 3) AddINode(dividend, mul_hi));
 170 
 171         // Shift over the (adjusted) mulhi
 172         if (shift_const != 0) {
 173           mul_hi = phase->transform(new (phase->C, 3) RShiftINode(mul_hi, phase->intcon(shift_const)));
 174         }
 175       } else {
 176         // No add is required, we can merge the shifts together.
 177         mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(N + shift_const)));
 178         mul_hi = phase->transform(new (phase->C, 2) ConvL2INode(mul_hi));
 179       }
 180 
 181       // Get a 0 or -1 from the sign of the dividend.
 182       Node *addend0 = mul_hi;
 183       Node *addend1 = phase->transform(new (phase->C, 3) RShiftINode(dividend, phase->intcon(N-1)));
 184 
 185       // If the divisor is negative, swap the order of the input addends;
 186       // this has the effect of negating the quotient.
 187       if (!d_pos) {
 188         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 189       }
 190 
 191       // Adjust the final quotient by subtracting -1 (adding 1)
 192       // from the mul_hi.
 193       q = new (phase->C, 3) SubINode(addend0, addend1);
 194     }
 195   }
 196 
 197   return q;
 198 }
 199 
 200 //---------------------magic_long_divide_constants-----------------------------
 201 // Compute magic multiplier and shift constant for converting a 64 bit divide
 202 // by constant into a multiply/shift/add series. Return false if calculations
 203 // fail.
 204 //
 205 // Borrowed almost verbatum from Hacker's Delight by Henry S. Warren, Jr. with
 206 // minor type name and parameter changes.  Adjusted to 64 bit word width.
 207 static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) {
 208   int64_t p;
 209   uint64_t ad, anc, delta, q1, r1, q2, r2, t;
 210   const uint64_t two63 = 0x8000000000000000LL;     // 2**63.
 211 
 212   ad = ABS(d);
 213   if (d == 0 || d == 1) return false;
 214   t = two63 + ((uint64_t)d >> 63);
 215   anc = t - 1 - t%ad;     // Absolute value of nc.
 216   p = 63;                 // Init. p.
 217   q1 = two63/anc;         // Init. q1 = 2**p/|nc|.
 218   r1 = two63 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
 219   q2 = two63/ad;          // Init. q2 = 2**p/|d|.
 220   r2 = two63 - q2*ad;     // Init. r2 = rem(2**p, |d|).
 221   do {
 222     p = p + 1;
 223     q1 = 2*q1;            // Update q1 = 2**p/|nc|.
 224     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
 225     if (r1 >= anc) {      // (Must be an unsigned
 226       q1 = q1 + 1;        // comparison here).
 227       r1 = r1 - anc;
 228     }
 229     q2 = 2*q2;            // Update q2 = 2**p/|d|.
 230     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
 231     if (r2 >= ad) {       // (Must be an unsigned
 232       q2 = q2 + 1;        // comparison here).
 233       r2 = r2 - ad;
 234     }
 235     delta = ad - r2;
 236   } while (q1 < delta || (q1 == delta && r1 == 0));
 237 
 238   M = q2 + 1;
 239   if (d < 0) M = -M;      // Magic number and
 240   s = p - 64;             // shift amount to return.
 241 
 242   return true;
 243 }
 244 
 245 //---------------------long_by_long_mulhi--------------------------------------
 246 // Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication
 247 static Node *long_by_long_mulhi( PhaseGVN *phase, Node *dividend, jlong magic_const) {
 248   // If the architecture supports a 64x64 mulhi, there is
 249   // no need to synthesize it in ideal nodes.
 250   if (Matcher::has_match_rule(Op_MulHiL)) {
 251     Node *v = phase->longcon(magic_const);
 252     return new (phase->C, 3) MulHiLNode(dividend, v);
 253   }
 254 
 255   const int N = 64;
 256 
 257   Node *u_hi = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N / 2)));
 258   Node *u_lo = phase->transform(new (phase->C, 3) AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
 259 
 260   Node *v_hi = phase->longcon(magic_const >> N/2);
 261   Node *v_lo = phase->longcon(magic_const & 0XFFFFFFFF);
 262 
 263   Node *hihi_product = phase->transform(new (phase->C, 3) MulLNode(u_hi, v_hi));
 264   Node *hilo_product = phase->transform(new (phase->C, 3) MulLNode(u_hi, v_lo));
 265   Node *lohi_product = phase->transform(new (phase->C, 3) MulLNode(u_lo, v_hi));
 266   Node *lolo_product = phase->transform(new (phase->C, 3) MulLNode(u_lo, v_lo));
 267 
 268   Node *t1 = phase->transform(new (phase->C, 3) URShiftLNode(lolo_product, phase->intcon(N / 2)));
 269   Node *t2 = phase->transform(new (phase->C, 3) AddLNode(hilo_product, t1));
 270 
 271   // Construct both t3 and t4 before transforming so t2 doesn't go dead
 272   // prematurely.
 273   Node *t3 = new (phase->C, 3) RShiftLNode(t2, phase->intcon(N / 2));
 274   Node *t4 = new (phase->C, 3) AndLNode(t2, phase->longcon(0xFFFFFFFF));
 275   t3 = phase->transform(t3);
 276   t4 = phase->transform(t4);
 277 
 278   Node *t5 = phase->transform(new (phase->C, 3) AddLNode(t4, lohi_product));
 279   Node *t6 = phase->transform(new (phase->C, 3) RShiftLNode(t5, phase->intcon(N / 2)));
 280   Node *t7 = phase->transform(new (phase->C, 3) AddLNode(t3, hihi_product));
 281 
 282   return new (phase->C, 3) AddLNode(t7, t6);
 283 }
 284 
 285 
 286 //--------------------------transform_long_divide------------------------------
 287 // Convert a division by constant divisor into an alternate Ideal graph.
 288 // Return NULL if no transformation occurs.
 289 static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {
 290   // Check for invalid divisors
 291   assert( divisor != 0L && divisor != min_jlong,
 292           "bad divisor for transforming to long multiply" );
 293 
 294   bool d_pos = divisor >= 0;
 295   jlong d = d_pos ? divisor : -divisor;
 296   const int N = 64;
 297 
 298   // Result
 299   Node *q = NULL;
 300 
 301   if (d == 1) {
 302     // division by +/- 1
 303     if (!d_pos) {
 304       // Just negate the value
 305       q = new (phase->C, 3) SubLNode(phase->longcon(0), dividend);
 306     }
 307   } else if ( is_power_of_2_long(d) ) {
 308 
 309     // division by +/- a power of 2
 310 
 311     // See if we can simply do a shift without rounding
 312     bool needs_rounding = true;
 313     const Type *dt = phase->type(dividend);
 314     const TypeLong *dtl = dt->isa_long();
 315 
 316     if (dtl && dtl->_lo > 0) {
 317       // we don't need to round a positive dividend
 318       needs_rounding = false;
 319     } else if( dividend->Opcode() == Op_AndL ) {
 320       // An AND mask of sufficient size clears the low bits and
 321       // I can avoid rounding.
 322       const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();
 323       if( andconl_t && andconl_t->is_con() ) {
 324         jlong andconl = andconl_t->get_con();
 325         if( andconl < 0 && is_power_of_2_long(-andconl) && (-andconl) >= d ) {
 326           dividend = dividend->in(1);
 327           needs_rounding = false;
 328         }
 329       }
 330     }
 331 
 332     // Add rounding to the shift to handle the sign bit
 333     int l = log2_long(d-1)+1;
 334     if (needs_rounding) {
 335       // Divide-by-power-of-2 can be made into a shift, but you have to do
 336       // more math for the rounding.  You need to add 0 for positive
 337       // numbers, and "i-1" for negative numbers.  Example: i=4, so the
 338       // shift is by 2.  You need to add 3 to negative dividends and 0 to
 339       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
 340       // (-2+3)>>2 becomes 0, etc.
 341 
 342       // Compute 0 or -1, based on sign bit
 343       Node *sign = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N - 1)));
 344       // Mask sign bit to the low sign bits
 345       Node *round = phase->transform(new (phase->C, 3) URShiftLNode(sign, phase->intcon(N - l)));
 346       // Round up before shifting
 347       dividend = phase->transform(new (phase->C, 3) AddLNode(dividend, round));
 348     }
 349 
 350     // Shift for division
 351     q = new (phase->C, 3) RShiftLNode(dividend, phase->intcon(l));
 352 
 353     if (!d_pos) {
 354       q = new (phase->C, 3) SubLNode(phase->longcon(0), phase->transform(q));
 355     }
 356   } else {
 357     // Attempt the jlong constant divide -> multiply transform found in
 358     //   "Division by Invariant Integers using Multiplication"
 359     //     by Granlund and Montgomery
 360     // See also "Hacker's Delight", chapter 10 by Warren.
 361 
 362     jlong magic_const;
 363     jint shift_const;
 364     if (magic_long_divide_constants(d, magic_const, shift_const)) {
 365       // Compute the high half of the dividend x magic multiplication
 366       Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
 367 
 368       // The high half of the 128-bit multiply is computed.
 369       if (magic_const < 0) {
 370         // The magic multiplier is too large for a 64 bit constant. We've adjusted
 371         // it down by 2^64, but have to add 1 dividend back in after the multiplication.
 372         // This handles the "overflow" case described by Granlund and Montgomery.
 373         mul_hi = phase->transform(new (phase->C, 3) AddLNode(dividend, mul_hi));
 374       }
 375 
 376       // Shift over the (adjusted) mulhi
 377       if (shift_const != 0) {
 378         mul_hi = phase->transform(new (phase->C, 3) RShiftLNode(mul_hi, phase->intcon(shift_const)));
 379       }
 380 
 381       // Get a 0 or -1 from the sign of the dividend.
 382       Node *addend0 = mul_hi;
 383       Node *addend1 = phase->transform(new (phase->C, 3) RShiftLNode(dividend, phase->intcon(N-1)));
 384 
 385       // If the divisor is negative, swap the order of the input addends;
 386       // this has the effect of negating the quotient.
 387       if (!d_pos) {
 388         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 389       }
 390 
 391       // Adjust the final quotient by subtracting -1 (adding 1)
 392       // from the mul_hi.
 393       q = new (phase->C, 3) SubLNode(addend0, addend1);
 394     }
 395   }
 396 
 397   return q;
 398 }
 399 
 400 //=============================================================================
 401 //------------------------------Identity---------------------------------------
 402 // If the divisor is 1, we are an identity on the dividend.
 403 Node *DivINode::Identity( PhaseTransform *phase ) {
 404   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
 405 }
 406 
 407 //------------------------------Idealize---------------------------------------
 408 // Divides can be changed to multiplies and/or shifts
 409 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 410   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 411   // Don't bother trying to transform a dead node
 412   if( in(0) && in(0)->is_top() )  return NULL;
 413 
 414   const Type *t = phase->type( in(2) );
 415   if( t == TypeInt::ONE )       // Identity?
 416     return NULL;                // Skip it
 417 
 418   const TypeInt *ti = t->isa_int();
 419   if( !ti ) return NULL;
 420   if( !ti->is_con() ) return NULL;
 421   jint i = ti->get_con();       // Get divisor
 422 
 423   if (i == 0) return NULL;      // Dividing by zero constant does not idealize
 424 
 425   set_req(0,NULL);              // Dividing by a not-zero constant; no faulting
 426 
 427   // Dividing by MININT does not optimize as a power-of-2 shift.
 428   if( i == min_jint ) return NULL;
 429 
 430   return transform_int_divide( phase, in(1), i );
 431 }
 432 
 433 //------------------------------Value------------------------------------------
 434 // A DivINode divides its inputs.  The third input is a Control input, used to
 435 // prevent hoisting the divide above an unsafe test.
 436 const Type *DivINode::Value( PhaseTransform *phase ) const {
 437   // Either input is TOP ==> the result is TOP
 438   const Type *t1 = phase->type( in(1) );
 439   const Type *t2 = phase->type( in(2) );
 440   if( t1 == Type::TOP ) return Type::TOP;
 441   if( t2 == Type::TOP ) return Type::TOP;
 442 
 443   // x/x == 1 since we always generate the dynamic divisor check for 0.
 444   if( phase->eqv( in(1), in(2) ) )
 445     return TypeInt::ONE;
 446 
 447   // Either input is BOTTOM ==> the result is the local BOTTOM
 448   const Type *bot = bottom_type();
 449   if( (t1 == bot) || (t2 == bot) ||
 450       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 451     return bot;
 452 
 453   // Divide the two numbers.  We approximate.
 454   // If divisor is a constant and not zero
 455   const TypeInt *i1 = t1->is_int();
 456   const TypeInt *i2 = t2->is_int();
 457   int widen = MAX2(i1->_widen, i2->_widen);
 458 
 459   if( i2->is_con() && i2->get_con() != 0 ) {
 460     int32 d = i2->get_con(); // Divisor
 461     jint lo, hi;
 462     if( d >= 0 ) {
 463       lo = i1->_lo/d;
 464       hi = i1->_hi/d;
 465     } else {
 466       if( d == -1 && i1->_lo == min_jint ) {
 467         // 'min_jint/-1' throws arithmetic exception during compilation
 468         lo = min_jint;
 469         // do not support holes, 'hi' must go to either min_jint or max_jint:
 470         // [min_jint, -10]/[-1,-1] ==> [min_jint] UNION [10,max_jint]
 471         hi = i1->_hi == min_jint ? min_jint : max_jint;
 472       } else {
 473         lo = i1->_hi/d;
 474         hi = i1->_lo/d;
 475       }
 476     }
 477     return TypeInt::make(lo, hi, widen);
 478   }
 479 
 480   // If the dividend is a constant
 481   if( i1->is_con() ) {
 482     int32 d = i1->get_con();
 483     if( d < 0 ) {
 484       if( d == min_jint ) {
 485         //  (-min_jint) == min_jint == (min_jint / -1)
 486         return TypeInt::make(min_jint, max_jint/2 + 1, widen);
 487       } else {
 488         return TypeInt::make(d, -d, widen);
 489       }
 490     }
 491     return TypeInt::make(-d, d, widen);
 492   }
 493 
 494   // Otherwise we give up all hope
 495   return TypeInt::INT;
 496 }
 497 
 498 
 499 //=============================================================================
 500 //------------------------------Identity---------------------------------------
 501 // If the divisor is 1, we are an identity on the dividend.
 502 Node *DivLNode::Identity( PhaseTransform *phase ) {
 503   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
 504 }
 505 
 506 //------------------------------Idealize---------------------------------------
 507 // Dividing by a power of 2 is a shift.
 508 Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) {
 509   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 510   // Don't bother trying to transform a dead node
 511   if( in(0) && in(0)->is_top() )  return NULL;
 512 
 513   const Type *t = phase->type( in(2) );
 514   if( t == TypeLong::ONE )      // Identity?
 515     return NULL;                // Skip it
 516 
 517   const TypeLong *tl = t->isa_long();
 518   if( !tl ) return NULL;
 519   if( !tl->is_con() ) return NULL;
 520   jlong l = tl->get_con();      // Get divisor
 521 
 522   if (l == 0) return NULL;      // Dividing by zero constant does not idealize
 523 
 524   set_req(0,NULL);              // Dividing by a not-zero constant; no faulting
 525 
 526   // Dividing by MININT does not optimize as a power-of-2 shift.
 527   if( l == min_jlong ) return NULL;
 528 
 529   return transform_long_divide( phase, in(1), l );
 530 }
 531 
 532 //------------------------------Value------------------------------------------
 533 // A DivLNode divides its inputs.  The third input is a Control input, used to
 534 // prevent hoisting the divide above an unsafe test.
 535 const Type *DivLNode::Value( PhaseTransform *phase ) const {
 536   // Either input is TOP ==> the result is TOP
 537   const Type *t1 = phase->type( in(1) );
 538   const Type *t2 = phase->type( in(2) );
 539   if( t1 == Type::TOP ) return Type::TOP;
 540   if( t2 == Type::TOP ) return Type::TOP;
 541 
 542   // x/x == 1 since we always generate the dynamic divisor check for 0.
 543   if( phase->eqv( in(1), in(2) ) )
 544     return TypeLong::ONE;
 545 
 546   // Either input is BOTTOM ==> the result is the local BOTTOM
 547   const Type *bot = bottom_type();
 548   if( (t1 == bot) || (t2 == bot) ||
 549       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 550     return bot;
 551 
 552   // Divide the two numbers.  We approximate.
 553   // If divisor is a constant and not zero
 554   const TypeLong *i1 = t1->is_long();
 555   const TypeLong *i2 = t2->is_long();
 556   int widen = MAX2(i1->_widen, i2->_widen);
 557 
 558   if( i2->is_con() && i2->get_con() != 0 ) {
 559     jlong d = i2->get_con();    // Divisor
 560     jlong lo, hi;
 561     if( d >= 0 ) {
 562       lo = i1->_lo/d;
 563       hi = i1->_hi/d;
 564     } else {
 565       if( d == CONST64(-1) && i1->_lo == min_jlong ) {
 566         // 'min_jlong/-1' throws arithmetic exception during compilation
 567         lo = min_jlong;
 568         // do not support holes, 'hi' must go to either min_jlong or max_jlong:
 569         // [min_jlong, -10]/[-1,-1] ==> [min_jlong] UNION [10,max_jlong]
 570         hi = i1->_hi == min_jlong ? min_jlong : max_jlong;
 571       } else {
 572         lo = i1->_hi/d;
 573         hi = i1->_lo/d;
 574       }
 575     }
 576     return TypeLong::make(lo, hi, widen);
 577   }
 578 
 579   // If the dividend is a constant
 580   if( i1->is_con() ) {
 581     jlong d = i1->get_con();
 582     if( d < 0 ) {
 583       if( d == min_jlong ) {
 584         //  (-min_jlong) == min_jlong == (min_jlong / -1)
 585         return TypeLong::make(min_jlong, max_jlong/2 + 1, widen);
 586       } else {
 587         return TypeLong::make(d, -d, widen);
 588       }
 589     }
 590     return TypeLong::make(-d, d, widen);
 591   }
 592 
 593   // Otherwise we give up all hope
 594   return TypeLong::LONG;
 595 }
 596 
 597 
 598 //=============================================================================
 599 //------------------------------Value------------------------------------------
 600 // An DivFNode divides its inputs.  The third input is a Control input, used to
 601 // prevent hoisting the divide above an unsafe test.
 602 const Type *DivFNode::Value( PhaseTransform *phase ) const {
 603   // Either input is TOP ==> the result is TOP
 604   const Type *t1 = phase->type( in(1) );
 605   const Type *t2 = phase->type( in(2) );
 606   if( t1 == Type::TOP ) return Type::TOP;
 607   if( t2 == Type::TOP ) return Type::TOP;
 608 
 609   // Either input is BOTTOM ==> the result is the local BOTTOM
 610   const Type *bot = bottom_type();
 611   if( (t1 == bot) || (t2 == bot) ||
 612       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 613     return bot;
 614 
 615   // x/x == 1, we ignore 0/0.
 616   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 617   // Does not work for variables because of NaN's
 618   if( phase->eqv( in(1), in(2) ) && t1->base() == Type::FloatCon)
 619     if (!g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) // could be negative ZERO or NaN
 620       return TypeF::ONE;
 621 
 622   if( t2 == TypeF::ONE )
 623     return t1;
 624 
 625   // If divisor is a constant and not zero, divide them numbers
 626   if( t1->base() == Type::FloatCon &&
 627       t2->base() == Type::FloatCon &&
 628       t2->getf() != 0.0 ) // could be negative zero
 629     return TypeF::make( t1->getf()/t2->getf() );
 630 
 631   // If the dividend is a constant zero
 632   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 633   // Test TypeF::ZERO is not sufficient as it could be negative zero
 634 
 635   if( t1 == TypeF::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0 )
 636     return TypeF::ZERO;
 637 
 638   // Otherwise we give up all hope
 639   return Type::FLOAT;
 640 }
 641 
 642 //------------------------------isA_Copy---------------------------------------
 643 // Dividing by self is 1.
 644 // If the divisor is 1, we are an identity on the dividend.
 645 Node *DivFNode::Identity( PhaseTransform *phase ) {
 646   return (phase->type( in(2) ) == TypeF::ONE) ? in(1) : this;
 647 }
 648 
 649 
 650 //------------------------------Idealize---------------------------------------
 651 Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 652   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 653   // Don't bother trying to transform a dead node
 654   if( in(0) && in(0)->is_top() )  return NULL;
 655 
 656   const Type *t2 = phase->type( in(2) );
 657   if( t2 == TypeF::ONE )         // Identity?
 658     return NULL;                // Skip it
 659 
 660   const TypeF *tf = t2->isa_float_constant();
 661   if( !tf ) return NULL;
 662   if( tf->base() != Type::FloatCon ) return NULL;
 663 
 664   // Check for out of range values
 665   if( tf->is_nan() || !tf->is_finite() ) return NULL;
 666 
 667   // Get the value
 668   float f = tf->getf();
 669   int exp;
 670 
 671   // Only for special case of dividing by a power of 2
 672   if( frexp((double)f, &exp) != 0.5 ) return NULL;
 673 
 674   // Limit the range of acceptable exponents
 675   if( exp < -126 || exp > 126 ) return NULL;
 676 
 677   // Compute the reciprocal
 678   float reciprocal = ((float)1.0) / f;
 679 
 680   assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 681 
 682   // return multiplication by the reciprocal
 683   return (new (phase->C, 3) MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
 684 }
 685 
 686 //=============================================================================
 687 //------------------------------Value------------------------------------------
 688 // An DivDNode divides its inputs.  The third input is a Control input, used to
 689 // prevent hoisting the divide above an unsafe test.
 690 const Type *DivDNode::Value( PhaseTransform *phase ) const {
 691   // Either input is TOP ==> the result is TOP
 692   const Type *t1 = phase->type( in(1) );
 693   const Type *t2 = phase->type( in(2) );
 694   if( t1 == Type::TOP ) return Type::TOP;
 695   if( t2 == Type::TOP ) return Type::TOP;
 696 
 697   // Either input is BOTTOM ==> the result is the local BOTTOM
 698   const Type *bot = bottom_type();
 699   if( (t1 == bot) || (t2 == bot) ||
 700       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 701     return bot;
 702 
 703   // x/x == 1, we ignore 0/0.
 704   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 705   // Does not work for variables because of NaN's
 706   if( phase->eqv( in(1), in(2) ) && t1->base() == Type::DoubleCon)
 707     if (!g_isnan(t1->getd()) && g_isfinite(t1->getd()) && t1->getd() != 0.0) // could be negative ZERO or NaN
 708       return TypeD::ONE;
 709 
 710   if( t2 == TypeD::ONE )
 711     return t1;
 712 
 713   // If divisor is a constant and not zero, divide them numbers
 714   if( t1->base() == Type::DoubleCon &&
 715       t2->base() == Type::DoubleCon &&
 716       t2->getd() != 0.0 ) // could be negative zero
 717     return TypeD::make( t1->getd()/t2->getd() );
 718 
 719   // If the dividend is a constant zero
 720   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 721   // Test TypeF::ZERO is not sufficient as it could be negative zero
 722   if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )
 723     return TypeD::ZERO;
 724 
 725   // Otherwise we give up all hope
 726   return Type::DOUBLE;
 727 }
 728 
 729 
 730 //------------------------------isA_Copy---------------------------------------
 731 // Dividing by self is 1.
 732 // If the divisor is 1, we are an identity on the dividend.
 733 Node *DivDNode::Identity( PhaseTransform *phase ) {
 734   return (phase->type( in(2) ) == TypeD::ONE) ? in(1) : this;
 735 }
 736 
 737 //------------------------------Idealize---------------------------------------
 738 Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 739   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 740   // Don't bother trying to transform a dead node
 741   if( in(0) && in(0)->is_top() )  return NULL;
 742 
 743   const Type *t2 = phase->type( in(2) );
 744   if( t2 == TypeD::ONE )         // Identity?
 745     return NULL;                // Skip it
 746 
 747   const TypeD *td = t2->isa_double_constant();
 748   if( !td ) return NULL;
 749   if( td->base() != Type::DoubleCon ) return NULL;
 750 
 751   // Check for out of range values
 752   if( td->is_nan() || !td->is_finite() ) return NULL;
 753 
 754   // Get the value
 755   double d = td->getd();
 756   int exp;
 757 
 758   // Only for special case of dividing by a power of 2
 759   if( frexp(d, &exp) != 0.5 ) return NULL;
 760 
 761   // Limit the range of acceptable exponents
 762   if( exp < -1021 || exp > 1022 ) return NULL;
 763 
 764   // Compute the reciprocal
 765   double reciprocal = 1.0 / d;
 766 
 767   assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 768 
 769   // return multiplication by the reciprocal
 770   return (new (phase->C, 3) MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
 771 }
 772 
 773 //=============================================================================
 774 //------------------------------Idealize---------------------------------------
 775 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 776   // Check for dead control input
 777   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
 778   // Don't bother trying to transform a dead node
 779   if( in(0) && in(0)->is_top() )  return NULL;
 780 
 781   // Get the modulus
 782   const Type *t = phase->type( in(2) );
 783   if( t == Type::TOP ) return NULL;
 784   const TypeInt *ti = t->is_int();
 785 
 786   // Check for useless control input
 787   // Check for excluding mod-zero case
 788   if( in(0) && (ti->_hi < 0 || ti->_lo > 0) ) {
 789     set_req(0, NULL);        // Yank control input
 790     return this;
 791   }
 792 
 793   // See if we are MOD'ing by 2^k or 2^k-1.
 794   if( !ti->is_con() ) return NULL;
 795   jint con = ti->get_con();
 796 
 797   Node *hook = new (phase->C, 1) Node(1);
 798 
 799   // First, special check for modulo 2^k-1
 800   if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
 801     uint k = exact_log2(con+1);  // Extract k
 802 
 803     // Basic algorithm by David Detlefs.  See fastmod_int.java for gory details.
 804     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*/};
 805     int trip_count = 1;
 806     if( k < ARRAY_SIZE(unroll_factor))  trip_count = unroll_factor[k];
 807 
 808     // If the unroll factor is not too large, and if conditional moves are
 809     // ok, then use this case
 810     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
 811       Node *x = in(1);            // Value being mod'd
 812       Node *divisor = in(2);      // Also is mask
 813 
 814       hook->init_req(0, x);       // Add a use to x to prevent him from dying
 815       // Generate code to reduce X rapidly to nearly 2^k-1.
 816       for( int i = 0; i < trip_count; i++ ) {
 817         Node *xl = phase->transform( new (phase->C, 3) AndINode(x,divisor) );
 818         Node *xh = phase->transform( new (phase->C, 3) RShiftINode(x,phase->intcon(k)) ); // Must be signed
 819         x = phase->transform( new (phase->C, 3) AddINode(xh,xl) );
 820         hook->set_req(0, x);
 821       }
 822 
 823       // Generate sign-fixup code.  Was original value positive?
 824       // int hack_res = (i >= 0) ? divisor : 1;
 825       Node *cmp1 = phase->transform( new (phase->C, 3) CmpINode( in(1), phase->intcon(0) ) );
 826       Node *bol1 = phase->transform( new (phase->C, 2) BoolNode( cmp1, BoolTest::ge ) );
 827       Node *cmov1= phase->transform( new (phase->C, 4) CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
 828       // if( x >= hack_res ) x -= divisor;
 829       Node *sub  = phase->transform( new (phase->C, 3) SubINode( x, divisor ) );
 830       Node *cmp2 = phase->transform( new (phase->C, 3) CmpINode( x, cmov1 ) );
 831       Node *bol2 = phase->transform( new (phase->C, 2) BoolNode( cmp2, BoolTest::ge ) );
 832       // Convention is to not transform the return value of an Ideal
 833       // since Ideal is expected to return a modified 'this' or a new node.
 834       Node *cmov2= new (phase->C, 4) CMoveINode(bol2, x, sub, TypeInt::INT);
 835       // cmov2 is now the mod
 836 
 837       // Now remove the bogus extra edges used to keep things alive
 838       if (can_reshape) {
 839         phase->is_IterGVN()->remove_dead_node(hook);
 840       } else {
 841         hook->set_req(0, NULL);   // Just yank bogus edge during Parse phase
 842       }
 843       return cmov2;
 844     }
 845   }
 846 
 847   // Fell thru, the unroll case is not appropriate. Transform the modulo
 848   // into a long multiply/int multiply/subtract case
 849 
 850   // Cannot handle mod 0, and min_jint isn't handled by the transform
 851   if( con == 0 || con == min_jint ) return NULL;
 852 
 853   // Get the absolute value of the constant; at this point, we can use this
 854   jint pos_con = (con >= 0) ? con : -con;
 855 
 856   // integer Mod 1 is always 0
 857   if( pos_con == 1 ) return new (phase->C, 1) ConINode(TypeInt::ZERO);
 858 
 859   int log2_con = -1;
 860 
 861   // If this is a power of two, they maybe we can mask it
 862   if( is_power_of_2(pos_con) ) {
 863     log2_con = log2_intptr((intptr_t)pos_con);
 864 
 865     const Type *dt = phase->type(in(1));
 866     const TypeInt *dti = dt->isa_int();
 867 
 868     // See if this can be masked, if the dividend is non-negative
 869     if( dti && dti->_lo >= 0 )
 870       return ( new (phase->C, 3) AndINode( in(1), phase->intcon( pos_con-1 ) ) );
 871   }
 872 
 873   // Save in(1) so that it cannot be changed or deleted
 874   hook->init_req(0, in(1));
 875 
 876   // Divide using the transform from DivI to MulL
 877   Node *result = transform_int_divide( phase, in(1), pos_con );
 878   if (result != NULL) {
 879     Node *divide = phase->transform(result);
 880 
 881     // Re-multiply, using a shift if this is a power of two
 882     Node *mult = NULL;
 883 
 884     if( log2_con >= 0 )
 885       mult = phase->transform( new (phase->C, 3) LShiftINode( divide, phase->intcon( log2_con ) ) );
 886     else
 887       mult = phase->transform( new (phase->C, 3) MulINode( divide, phase->intcon( pos_con ) ) );
 888 
 889     // Finally, subtract the multiplied divided value from the original
 890     result = new (phase->C, 3) SubINode( in(1), mult );
 891   }
 892 
 893   // Now remove the bogus extra edges used to keep things alive
 894   if (can_reshape) {
 895     phase->is_IterGVN()->remove_dead_node(hook);
 896   } else {
 897     hook->set_req(0, NULL);       // Just yank bogus edge during Parse phase
 898   }
 899 
 900   // return the value
 901   return result;
 902 }
 903 
 904 //------------------------------Value------------------------------------------
 905 const Type *ModINode::Value( PhaseTransform *phase ) const {
 906   // Either input is TOP ==> the result is TOP
 907   const Type *t1 = phase->type( in(1) );
 908   const Type *t2 = phase->type( in(2) );
 909   if( t1 == Type::TOP ) return Type::TOP;
 910   if( t2 == Type::TOP ) return Type::TOP;
 911 
 912   // We always generate the dynamic check for 0.
 913   // 0 MOD X is 0
 914   if( t1 == TypeInt::ZERO ) return TypeInt::ZERO;
 915   // X MOD X is 0
 916   if( phase->eqv( in(1), in(2) ) ) return TypeInt::ZERO;
 917 
 918   // Either input is BOTTOM ==> the result is the local BOTTOM
 919   const Type *bot = bottom_type();
 920   if( (t1 == bot) || (t2 == bot) ||
 921       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 922     return bot;
 923 
 924   const TypeInt *i1 = t1->is_int();
 925   const TypeInt *i2 = t2->is_int();
 926   if( !i1->is_con() || !i2->is_con() ) {
 927     if( i1->_lo >= 0 && i2->_lo >= 0 )
 928       return TypeInt::POS;
 929     // If both numbers are not constants, we know little.
 930     return TypeInt::INT;
 931   }
 932   // Mod by zero?  Throw exception at runtime!
 933   if( !i2->get_con() ) return TypeInt::POS;
 934 
 935   // We must be modulo'ing 2 float constants.
 936   // Check for min_jint % '-1', result is defined to be '0'.
 937   if( i1->get_con() == min_jint && i2->get_con() == -1 )
 938     return TypeInt::ZERO;
 939 
 940   return TypeInt::make( i1->get_con() % i2->get_con() );
 941 }
 942 
 943 
 944 //=============================================================================
 945 //------------------------------Idealize---------------------------------------
 946 Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 947   // Check for dead control input
 948   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
 949   // Don't bother trying to transform a dead node
 950   if( in(0) && in(0)->is_top() )  return NULL;
 951 
 952   // Get the modulus
 953   const Type *t = phase->type( in(2) );
 954   if( t == Type::TOP ) return NULL;
 955   const TypeLong *tl = t->is_long();
 956 
 957   // Check for useless control input
 958   // Check for excluding mod-zero case
 959   if( in(0) && (tl->_hi < 0 || tl->_lo > 0) ) {
 960     set_req(0, NULL);        // Yank control input
 961     return this;
 962   }
 963 
 964   // See if we are MOD'ing by 2^k or 2^k-1.
 965   if( !tl->is_con() ) return NULL;
 966   jlong con = tl->get_con();
 967 
 968   Node *hook = new (phase->C, 1) Node(1);
 969 
 970   // Expand mod
 971   if( con >= 0 && con < max_jlong && is_power_of_2_long(con+1) ) {
 972     uint k = log2_long(con);       // Extract k
 973 
 974     // Basic algorithm by David Detlefs.  See fastmod_long.java for gory details.
 975     // Used to help a popular random number generator which does a long-mod
 976     // of 2^31-1 and shows up in SpecJBB and SciMark.
 977     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*/};
 978     int trip_count = 1;
 979     if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
 980 
 981     // If the unroll factor is not too large, and if conditional moves are
 982     // ok, then use this case
 983     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
 984       Node *x = in(1);            // Value being mod'd
 985       Node *divisor = in(2);      // Also is mask
 986 
 987       hook->init_req(0, x);       // Add a use to x to prevent him from dying
 988       // Generate code to reduce X rapidly to nearly 2^k-1.
 989       for( int i = 0; i < trip_count; i++ ) {
 990         Node *xl = phase->transform( new (phase->C, 3) AndLNode(x,divisor) );
 991         Node *xh = phase->transform( new (phase->C, 3) RShiftLNode(x,phase->intcon(k)) ); // Must be signed
 992         x = phase->transform( new (phase->C, 3) AddLNode(xh,xl) );
 993         hook->set_req(0, x);    // Add a use to x to prevent him from dying
 994       }
 995 
 996       // Generate sign-fixup code.  Was original value positive?
 997       // long hack_res = (i >= 0) ? divisor : CONST64(1);
 998       Node *cmp1 = phase->transform( new (phase->C, 3) CmpLNode( in(1), phase->longcon(0) ) );
 999       Node *bol1 = phase->transform( new (phase->C, 2) BoolNode( cmp1, BoolTest::ge ) );
1000       Node *cmov1= phase->transform( new (phase->C, 4) CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
1001       // if( x >= hack_res ) x -= divisor;
1002       Node *sub  = phase->transform( new (phase->C, 3) SubLNode( x, divisor ) );
1003       Node *cmp2 = phase->transform( new (phase->C, 3) CmpLNode( x, cmov1 ) );
1004       Node *bol2 = phase->transform( new (phase->C, 2) BoolNode( cmp2, BoolTest::ge ) );
1005       // Convention is to not transform the return value of an Ideal
1006       // since Ideal is expected to return a modified 'this' or a new node.
1007       Node *cmov2= new (phase->C, 4) CMoveLNode(bol2, x, sub, TypeLong::LONG);
1008       // cmov2 is now the mod
1009 
1010       // Now remove the bogus extra edges used to keep things alive
1011       if (can_reshape) {
1012         phase->is_IterGVN()->remove_dead_node(hook);
1013       } else {
1014         hook->set_req(0, NULL);   // Just yank bogus edge during Parse phase
1015       }
1016       return cmov2;
1017     }
1018   }
1019 
1020   // Fell thru, the unroll case is not appropriate. Transform the modulo
1021   // into a long multiply/int multiply/subtract case
1022 
1023   // Cannot handle mod 0, and min_jint isn't handled by the transform
1024   if( con == 0 || con == min_jlong ) return NULL;
1025 
1026   // Get the absolute value of the constant; at this point, we can use this
1027   jlong pos_con = (con >= 0) ? con : -con;
1028 
1029   // integer Mod 1 is always 0
1030   if( pos_con == 1 ) return new (phase->C, 1) ConLNode(TypeLong::ZERO);
1031 
1032   int log2_con = -1;
1033 
1034   // If this is a power of two, they maybe we can mask it
1035   if( is_power_of_2_long(pos_con) ) {
1036     log2_con = log2_long(pos_con);
1037 
1038     const Type *dt = phase->type(in(1));
1039     const TypeLong *dtl = dt->isa_long();
1040 
1041     // See if this can be masked, if the dividend is non-negative
1042     if( dtl && dtl->_lo >= 0 )
1043       return ( new (phase->C, 3) AndLNode( in(1), phase->longcon( pos_con-1 ) ) );
1044   }
1045 
1046   // Save in(1) so that it cannot be changed or deleted
1047   hook->init_req(0, in(1));
1048 
1049   // Divide using the transform from DivI to MulL
1050   Node *result = transform_long_divide( phase, in(1), pos_con );
1051   if (result != NULL) {
1052     Node *divide = phase->transform(result);
1053 
1054     // Re-multiply, using a shift if this is a power of two
1055     Node *mult = NULL;
1056 
1057     if( log2_con >= 0 )
1058       mult = phase->transform( new (phase->C, 3) LShiftLNode( divide, phase->intcon( log2_con ) ) );
1059     else
1060       mult = phase->transform( new (phase->C, 3) MulLNode( divide, phase->longcon( pos_con ) ) );
1061 
1062     // Finally, subtract the multiplied divided value from the original
1063     result = new (phase->C, 3) SubLNode( in(1), mult );
1064   }
1065 
1066   // Now remove the bogus extra edges used to keep things alive
1067   if (can_reshape) {
1068     phase->is_IterGVN()->remove_dead_node(hook);
1069   } else {
1070     hook->set_req(0, NULL);       // Just yank bogus edge during Parse phase
1071   }
1072 
1073   // return the value
1074   return result;
1075 }
1076 
1077 //------------------------------Value------------------------------------------
1078 const Type *ModLNode::Value( PhaseTransform *phase ) const {
1079   // Either input is TOP ==> the result is TOP
1080   const Type *t1 = phase->type( in(1) );
1081   const Type *t2 = phase->type( in(2) );
1082   if( t1 == Type::TOP ) return Type::TOP;
1083   if( t2 == Type::TOP ) return Type::TOP;
1084 
1085   // We always generate the dynamic check for 0.
1086   // 0 MOD X is 0
1087   if( t1 == TypeLong::ZERO ) return TypeLong::ZERO;
1088   // X MOD X is 0
1089   if( phase->eqv( in(1), in(2) ) ) return TypeLong::ZERO;
1090 
1091   // Either input is BOTTOM ==> the result is the local BOTTOM
1092   const Type *bot = bottom_type();
1093   if( (t1 == bot) || (t2 == bot) ||
1094       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1095     return bot;
1096 
1097   const TypeLong *i1 = t1->is_long();
1098   const TypeLong *i2 = t2->is_long();
1099   if( !i1->is_con() || !i2->is_con() ) {
1100     if( i1->_lo >= CONST64(0) && i2->_lo >= CONST64(0) )
1101       return TypeLong::POS;
1102     // If both numbers are not constants, we know little.
1103     return TypeLong::LONG;
1104   }
1105   // Mod by zero?  Throw exception at runtime!
1106   if( !i2->get_con() ) return TypeLong::POS;
1107 
1108   // We must be modulo'ing 2 float constants.
1109   // Check for min_jint % '-1', result is defined to be '0'.
1110   if( i1->get_con() == min_jlong && i2->get_con() == -1 )
1111     return TypeLong::ZERO;
1112 
1113   return TypeLong::make( i1->get_con() % i2->get_con() );
1114 }
1115 
1116 
1117 //=============================================================================
1118 //------------------------------Value------------------------------------------
1119 const Type *ModFNode::Value( PhaseTransform *phase ) const {
1120   // Either input is TOP ==> the result is TOP
1121   const Type *t1 = phase->type( in(1) );
1122   const Type *t2 = phase->type( in(2) );
1123   if( t1 == Type::TOP ) return Type::TOP;
1124   if( t2 == Type::TOP ) return Type::TOP;
1125 
1126   // Either input is BOTTOM ==> the result is the local BOTTOM
1127   const Type *bot = bottom_type();
1128   if( (t1 == bot) || (t2 == bot) ||
1129       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1130     return bot;
1131 
1132   // If either number is not a constant, we know nothing.
1133   if ((t1->base() != Type::FloatCon) || (t2->base() != Type::FloatCon)) {
1134     return Type::FLOAT;         // note: x%x can be either NaN or 0
1135   }
1136 
1137   float f1 = t1->getf();
1138   float f2 = t2->getf();
1139   jint  x1 = jint_cast(f1);     // note:  *(int*)&f1, not just (int)f1
1140   jint  x2 = jint_cast(f2);
1141 
1142   // If either is a NaN, return an input NaN
1143   if (g_isnan(f1))    return t1;
1144   if (g_isnan(f2))    return t2;
1145 
1146   // If an operand is infinity or the divisor is +/- zero, punt.
1147   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jint)
1148     return Type::FLOAT;
1149 
1150   // We must be modulo'ing 2 float constants.
1151   // Make sure that the sign of the fmod is equal to the sign of the dividend
1152   jint xr = jint_cast(fmod(f1, f2));
1153   if ((x1 ^ xr) < 0) {
1154     xr ^= min_jint;
1155   }
1156 
1157   return TypeF::make(jfloat_cast(xr));
1158 }
1159 
1160 
1161 //=============================================================================
1162 //------------------------------Value------------------------------------------
1163 const Type *ModDNode::Value( PhaseTransform *phase ) const {
1164   // Either input is TOP ==> the result is TOP
1165   const Type *t1 = phase->type( in(1) );
1166   const Type *t2 = phase->type( in(2) );
1167   if( t1 == Type::TOP ) return Type::TOP;
1168   if( t2 == Type::TOP ) return Type::TOP;
1169 
1170   // Either input is BOTTOM ==> the result is the local BOTTOM
1171   const Type *bot = bottom_type();
1172   if( (t1 == bot) || (t2 == bot) ||
1173       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1174     return bot;
1175 
1176   // If either number is not a constant, we know nothing.
1177   if ((t1->base() != Type::DoubleCon) || (t2->base() != Type::DoubleCon)) {
1178     return Type::DOUBLE;        // note: x%x can be either NaN or 0
1179   }
1180 
1181   double f1 = t1->getd();
1182   double f2 = t2->getd();
1183   jlong  x1 = jlong_cast(f1);   // note:  *(long*)&f1, not just (long)f1
1184   jlong  x2 = jlong_cast(f2);
1185 
1186   // If either is a NaN, return an input NaN
1187   if (g_isnan(f1))    return t1;
1188   if (g_isnan(f2))    return t2;
1189 
1190   // If an operand is infinity or the divisor is +/- zero, punt.
1191   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jlong)
1192     return Type::DOUBLE;
1193 
1194   // We must be modulo'ing 2 double constants.
1195   // Make sure that the sign of the fmod is equal to the sign of the dividend
1196   jlong xr = jlong_cast(fmod(f1, f2));
1197   if ((x1 ^ xr) < 0) {
1198     xr ^= min_jlong;
1199   }
1200 
1201   return TypeD::make(jdouble_cast(xr));
1202 }
1203 
1204 //=============================================================================
1205 
1206 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
1207   init_req(0, c);
1208   init_req(1, dividend);
1209   init_req(2, divisor);
1210 }
1211 
1212 //------------------------------make------------------------------------------
1213 DivModINode* DivModINode::make(Compile* C, Node* div_or_mod) {
1214   Node* n = div_or_mod;
1215   assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
1216          "only div or mod input pattern accepted");
1217 
1218   DivModINode* divmod = new (C, 3) DivModINode(n->in(0), n->in(1), n->in(2));
1219   Node*        dproj  = new (C, 1) ProjNode(divmod, DivModNode::div_proj_num);
1220   Node*        mproj  = new (C, 1) ProjNode(divmod, DivModNode::mod_proj_num);
1221   return divmod;
1222 }
1223 
1224 //------------------------------make------------------------------------------
1225 DivModLNode* DivModLNode::make(Compile* C, Node* div_or_mod) {
1226   Node* n = div_or_mod;
1227   assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
1228          "only div or mod input pattern accepted");
1229 
1230   DivModLNode* divmod = new (C, 3) DivModLNode(n->in(0), n->in(1), n->in(2));
1231   Node*        dproj  = new (C, 1) ProjNode(divmod, DivModNode::div_proj_num);
1232   Node*        mproj  = new (C, 1) ProjNode(divmod, DivModNode::mod_proj_num);
1233   return divmod;
1234 }
1235 
1236 //------------------------------match------------------------------------------
1237 // return result(s) along with their RegMask info
1238 Node *DivModINode::match( const ProjNode *proj, const Matcher *match ) {
1239   uint ideal_reg = proj->ideal_reg();
1240   RegMask rm;
1241   if (proj->_con == div_proj_num) {
1242     rm = match->divI_proj_mask();
1243   } else {
1244     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1245     rm = match->modI_proj_mask();
1246   }
1247   return new (match->C, 1)MachProjNode(this, proj->_con, rm, ideal_reg);
1248 }
1249 
1250 
1251 //------------------------------match------------------------------------------
1252 // return result(s) along with their RegMask info
1253 Node *DivModLNode::match( const ProjNode *proj, const Matcher *match ) {
1254   uint ideal_reg = proj->ideal_reg();
1255   RegMask rm;
1256   if (proj->_con == div_proj_num) {
1257     rm = match->divL_proj_mask();
1258   } else {
1259     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1260     rm = match->modL_proj_mask();
1261   }
1262   return new (match->C, 1)MachProjNode(this, proj->_con, rm, ideal_reg);
1263 }