1 /*
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   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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   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.
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   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).
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  17  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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  20  * or visit www.oracle.com if you need additional information or have any
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  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 = nullptr;
 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   //
 270   // int mulhs(int u, int v) {
 271   //    unsigned u0, v0, w0;
 272   //    int u1, v1, w1, w2, t;
 273   //
 274   //    u0 = u & 0xFFFF;  u1 = u >> 16;
 275   //    v0 = v & 0xFFFF;  v1 = v >> 16;
 276   //    w0 = u0*v0;
 277   //    t  = u1*v0 + (w0 >> 16);
 278   //    w1 = t & 0xFFFF;
 279   //    w2 = t >> 16;
 280   //    w1 = u0*v1 + w1;
 281   //    return u1*v1 + w2 + (w1 >> 16);
 282   // }
 283   //
 284   // Note: The version above is for 32x32 multiplications, while the
 285   // following inline comments are adapted to 64x64.
 286 
 287   const int N = 64;
 288 
 289   // Dummy node to keep intermediate nodes alive during construction
 290   Node* hook = new Node(4);
 291 
 292   // u0 = u & 0xFFFFFFFF;  u1 = u >> 32;
 293   Node* u0 = phase->transform(new AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
 294   Node* u1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N / 2)));
 295   hook->init_req(0, u0);
 296   hook->init_req(1, u1);
 297 
 298   // v0 = v & 0xFFFFFFFF;  v1 = v >> 32;
 299   Node* v0 = phase->longcon(magic_const & 0xFFFFFFFF);
 300   Node* v1 = phase->longcon(magic_const >> (N / 2));
 301 
 302   // w0 = u0*v0;
 303   Node* w0 = phase->transform(new MulLNode(u0, v0));
 304 
 305   // t = u1*v0 + (w0 >> 32);
 306   Node* u1v0 = phase->transform(new MulLNode(u1, v0));
 307   Node* temp = phase->transform(new URShiftLNode(w0, phase->intcon(N / 2)));
 308   Node* t    = phase->transform(new AddLNode(u1v0, temp));
 309   hook->init_req(2, t);
 310 
 311   // w1 = t & 0xFFFFFFFF;
 312   Node* w1 = phase->transform(new AndLNode(t, phase->longcon(0xFFFFFFFF)));
 313   hook->init_req(3, w1);
 314 
 315   // w2 = t >> 32;
 316   Node* w2 = phase->transform(new RShiftLNode(t, phase->intcon(N / 2)));
 317 
 318   // w1 = u0*v1 + w1;
 319   Node* u0v1 = phase->transform(new MulLNode(u0, v1));
 320   w1         = phase->transform(new AddLNode(u0v1, w1));
 321 
 322   // return u1*v1 + w2 + (w1 >> 32);
 323   Node* u1v1  = phase->transform(new MulLNode(u1, v1));
 324   Node* temp1 = phase->transform(new AddLNode(u1v1, w2));
 325   Node* temp2 = phase->transform(new RShiftLNode(w1, phase->intcon(N / 2)));
 326 
 327   // Remove the bogus extra edges used to keep things alive
 328   hook->destruct(phase);
 329 
 330   return new AddLNode(temp1, temp2);
 331 }
 332 
 333 
 334 //--------------------------transform_long_divide------------------------------
 335 // Convert a division by constant divisor into an alternate Ideal graph.
 336 // Return null if no transformation occurs.
 337 static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {
 338   // Check for invalid divisors
 339   assert( divisor != 0L && divisor != min_jlong,
 340           "bad divisor for transforming to long multiply" );
 341 
 342   bool d_pos = divisor >= 0;
 343   jlong d = d_pos ? divisor : -divisor;
 344   const int N = 64;
 345 
 346   // Result
 347   Node *q = nullptr;
 348 
 349   if (d == 1) {
 350     // division by +/- 1
 351     if (!d_pos) {
 352       // Just negate the value
 353       q = new SubLNode(phase->longcon(0), dividend);
 354     }
 355   } else if ( is_power_of_2(d) ) {
 356 
 357     // division by +/- a power of 2
 358 
 359     // See if we can simply do a shift without rounding
 360     bool needs_rounding = true;
 361     const Type *dt = phase->type(dividend);
 362     const TypeLong *dtl = dt->isa_long();
 363 
 364     if (dtl && dtl->_lo > 0) {
 365       // we don't need to round a positive dividend
 366       needs_rounding = false;
 367     } else if( dividend->Opcode() == Op_AndL ) {
 368       // An AND mask of sufficient size clears the low bits and
 369       // I can avoid rounding.
 370       const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();
 371       if( andconl_t && andconl_t->is_con() ) {
 372         jlong andconl = andconl_t->get_con();
 373         if( andconl < 0 && is_power_of_2(-andconl) && (-andconl) >= d ) {
 374           if( (-andconl) == d ) // Remove AND if it clears bits which will be shifted
 375             dividend = dividend->in(1);
 376           needs_rounding = false;
 377         }
 378       }
 379     }
 380 
 381     // Add rounding to the shift to handle the sign bit
 382     int l = log2i_graceful(d - 1) + 1;
 383     if (needs_rounding) {
 384       // Divide-by-power-of-2 can be made into a shift, but you have to do
 385       // more math for the rounding.  You need to add 0 for positive
 386       // numbers, and "i-1" for negative numbers.  Example: i=4, so the
 387       // shift is by 2.  You need to add 3 to negative dividends and 0 to
 388       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
 389       // (-2+3)>>2 becomes 0, etc.
 390 
 391       // Compute 0 or -1, based on sign bit
 392       Node *sign = phase->transform(new RShiftLNode(dividend, phase->intcon(N - 1)));
 393       // Mask sign bit to the low sign bits
 394       Node *round = phase->transform(new URShiftLNode(sign, phase->intcon(N - l)));
 395       // Round up before shifting
 396       dividend = phase->transform(new AddLNode(dividend, round));
 397     }
 398 
 399     // Shift for division
 400     q = new RShiftLNode(dividend, phase->intcon(l));
 401 
 402     if (!d_pos) {
 403       q = new SubLNode(phase->longcon(0), phase->transform(q));
 404     }
 405   } else if ( !Matcher::use_asm_for_ldiv_by_con(d) ) { // Use hardware DIV instruction when
 406                                                        // it is faster than code generated below.
 407     // Attempt the jlong constant divide -> multiply transform found in
 408     //   "Division by Invariant Integers using Multiplication"
 409     //     by Granlund and Montgomery
 410     // See also "Hacker's Delight", chapter 10 by Warren.
 411 
 412     jlong magic_const;
 413     jint shift_const;
 414     if (magic_long_divide_constants(d, magic_const, shift_const)) {
 415       // Compute the high half of the dividend x magic multiplication
 416       Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
 417 
 418       // The high half of the 128-bit multiply is computed.
 419       if (magic_const < 0) {
 420         // The magic multiplier is too large for a 64 bit constant. We've adjusted
 421         // it down by 2^64, but have to add 1 dividend back in after the multiplication.
 422         // This handles the "overflow" case described by Granlund and Montgomery.
 423         mul_hi = phase->transform(new AddLNode(dividend, mul_hi));
 424       }
 425 
 426       // Shift over the (adjusted) mulhi
 427       if (shift_const != 0) {
 428         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(shift_const)));
 429       }
 430 
 431       // Get a 0 or -1 from the sign of the dividend.
 432       Node *addend0 = mul_hi;
 433       Node *addend1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N-1)));
 434 
 435       // If the divisor is negative, swap the order of the input addends;
 436       // this has the effect of negating the quotient.
 437       if (!d_pos) {
 438         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 439       }
 440 
 441       // Adjust the final quotient by subtracting -1 (adding 1)
 442       // from the mul_hi.
 443       q = new SubLNode(addend0, addend1);
 444     }
 445   }
 446 
 447   return q;
 448 }
 449 
 450 template <typename TypeClass, typename Unsigned>
 451 Node* unsigned_div_ideal(PhaseGVN* phase, bool can_reshape, Node* div) {
 452   // Check for dead control input
 453   if (div->in(0) != nullptr && div->remove_dead_region(phase, can_reshape)) {
 454     return div;
 455   }
 456   // Don't bother trying to transform a dead node
 457   if (div->in(0) != nullptr && div->in(0)->is_top()) {
 458     return nullptr;
 459   }
 460 
 461   const Type* t = phase->type(div->in(2));
 462   if (t == Type::TOP) {
 463     return nullptr;
 464   }
 465   const TypeClass* type_divisor = t->cast<TypeClass>();
 466 
 467   // Check for useless control input
 468   // Check for excluding div-zero case
 469   if (div->in(0) != nullptr && (type_divisor->_hi < 0 || type_divisor->_lo > 0)) {
 470     div->set_req(0, nullptr); // Yank control input
 471     return div;
 472   }
 473 
 474   if (!type_divisor->is_con()) {
 475     return nullptr;
 476   }
 477   Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con()); // Get divisor
 478 
 479   if (divisor == 0 || divisor == 1) {
 480     return nullptr; // Dividing by zero constant does not idealize
 481   }
 482 
 483   if (is_power_of_2(divisor)) {
 484     return make_urshift<TypeClass>(div->in(1), phase->intcon(log2i_graceful(divisor)));
 485   }
 486 
 487   return nullptr;
 488 }
 489 
 490 
 491 //=============================================================================
 492 //------------------------------Identity---------------------------------------
 493 // If the divisor is 1, we are an identity on the dividend.
 494 Node* DivINode::Identity(PhaseGVN* phase) {
 495   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
 496 }
 497 
 498 //------------------------------Idealize---------------------------------------
 499 // Divides can be changed to multiplies and/or shifts
 500 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 501   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 502   // Don't bother trying to transform a dead node
 503   if( in(0) && in(0)->is_top() )  return nullptr;
 504 
 505   const Type *t = phase->type( in(2) );
 506   if( t == TypeInt::ONE )      // Identity?
 507     return nullptr;            // Skip it
 508 
 509   const TypeInt *ti = t->isa_int();
 510   if( !ti ) return nullptr;
 511 
 512   // Check for useless control input
 513   // Check for excluding div-zero case
 514   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
 515     set_req(0, nullptr);           // Yank control input
 516     return this;
 517   }
 518 
 519   if( !ti->is_con() ) return nullptr;
 520   jint i = ti->get_con();       // Get divisor
 521 
 522   if (i == 0) return nullptr;   // Dividing by zero constant does not idealize
 523 
 524   // Dividing by MININT does not optimize as a power-of-2 shift.
 525   if( i == min_jint ) return nullptr;
 526 
 527   return transform_int_divide( phase, in(1), i );
 528 }
 529 
 530 //------------------------------Value------------------------------------------
 531 // A DivINode divides its inputs.  The third input is a Control input, used to
 532 // prevent hoisting the divide above an unsafe test.
 533 const Type* DivINode::Value(PhaseGVN* phase) const {
 534   // Either input is TOP ==> the result is TOP
 535   const Type *t1 = phase->type( in(1) );
 536   const Type *t2 = phase->type( in(2) );
 537   if( t1 == Type::TOP ) return Type::TOP;
 538   if( t2 == Type::TOP ) return Type::TOP;
 539 
 540   // x/x == 1 since we always generate the dynamic divisor check for 0.
 541   if (in(1) == in(2)) {
 542     return TypeInt::ONE;
 543   }
 544 
 545   // Either input is BOTTOM ==> the result is the local BOTTOM
 546   const Type *bot = bottom_type();
 547   if( (t1 == bot) || (t2 == bot) ||
 548       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 549     return bot;
 550 
 551   // Divide the two numbers.  We approximate.
 552   // If divisor is a constant and not zero
 553   const TypeInt *i1 = t1->is_int();
 554   const TypeInt *i2 = t2->is_int();
 555   int widen = MAX2(i1->_widen, i2->_widen);
 556 
 557   if( i2->is_con() && i2->get_con() != 0 ) {
 558     int32_t d = i2->get_con(); // Divisor
 559     jint lo, hi;
 560     if( d >= 0 ) {
 561       lo = i1->_lo/d;
 562       hi = i1->_hi/d;
 563     } else {
 564       if( d == -1 && i1->_lo == min_jint ) {
 565         // 'min_jint/-1' throws arithmetic exception during compilation
 566         lo = min_jint;
 567         // do not support holes, 'hi' must go to either min_jint or max_jint:
 568         // [min_jint, -10]/[-1,-1] ==> [min_jint] UNION [10,max_jint]
 569         hi = i1->_hi == min_jint ? min_jint : max_jint;
 570       } else {
 571         lo = i1->_hi/d;
 572         hi = i1->_lo/d;
 573       }
 574     }
 575     return TypeInt::make(lo, hi, widen);
 576   }
 577 
 578   // If the dividend is a constant
 579   if( i1->is_con() ) {
 580     int32_t d = i1->get_con();
 581     if( d < 0 ) {
 582       if( d == min_jint ) {
 583         //  (-min_jint) == min_jint == (min_jint / -1)
 584         return TypeInt::make(min_jint, max_jint/2 + 1, widen);
 585       } else {
 586         return TypeInt::make(d, -d, widen);
 587       }
 588     }
 589     return TypeInt::make(-d, d, widen);
 590   }
 591 
 592   // Otherwise we give up all hope
 593   return TypeInt::INT;
 594 }
 595 
 596 
 597 //=============================================================================
 598 //------------------------------Identity---------------------------------------
 599 // If the divisor is 1, we are an identity on the dividend.
 600 Node* DivLNode::Identity(PhaseGVN* phase) {
 601   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
 602 }
 603 
 604 //------------------------------Idealize---------------------------------------
 605 // Dividing by a power of 2 is a shift.
 606 Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) {
 607   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 608   // Don't bother trying to transform a dead node
 609   if( in(0) && in(0)->is_top() )  return nullptr;
 610 
 611   const Type *t = phase->type( in(2) );
 612   if( t == TypeLong::ONE )      // Identity?
 613     return nullptr;             // Skip it
 614 
 615   const TypeLong *tl = t->isa_long();
 616   if( !tl ) return nullptr;
 617 
 618   // Check for useless control input
 619   // Check for excluding div-zero case
 620   if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
 621     set_req(0, nullptr);         // Yank control input
 622     return this;
 623   }
 624 
 625   if( !tl->is_con() ) return nullptr;
 626   jlong l = tl->get_con();      // Get divisor
 627 
 628   if (l == 0) return nullptr;   // Dividing by zero constant does not idealize
 629 
 630   // Dividing by MINLONG does not optimize as a power-of-2 shift.
 631   if( l == min_jlong ) return nullptr;
 632 
 633   return transform_long_divide( phase, in(1), l );
 634 }
 635 
 636 //------------------------------Value------------------------------------------
 637 // A DivLNode divides its inputs.  The third input is a Control input, used to
 638 // prevent hoisting the divide above an unsafe test.
 639 const Type* DivLNode::Value(PhaseGVN* phase) const {
 640   // Either input is TOP ==> the result is TOP
 641   const Type *t1 = phase->type( in(1) );
 642   const Type *t2 = phase->type( in(2) );
 643   if( t1 == Type::TOP ) return Type::TOP;
 644   if( t2 == Type::TOP ) return Type::TOP;
 645 
 646   // x/x == 1 since we always generate the dynamic divisor check for 0.
 647   if (in(1) == in(2)) {
 648     return TypeLong::ONE;
 649   }
 650 
 651   // Either input is BOTTOM ==> the result is the local BOTTOM
 652   const Type *bot = bottom_type();
 653   if( (t1 == bot) || (t2 == bot) ||
 654       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 655     return bot;
 656 
 657   // Divide the two numbers.  We approximate.
 658   // If divisor is a constant and not zero
 659   const TypeLong *i1 = t1->is_long();
 660   const TypeLong *i2 = t2->is_long();
 661   int widen = MAX2(i1->_widen, i2->_widen);
 662 
 663   if( i2->is_con() && i2->get_con() != 0 ) {
 664     jlong d = i2->get_con();    // Divisor
 665     jlong lo, hi;
 666     if( d >= 0 ) {
 667       lo = i1->_lo/d;
 668       hi = i1->_hi/d;
 669     } else {
 670       if( d == CONST64(-1) && i1->_lo == min_jlong ) {
 671         // 'min_jlong/-1' throws arithmetic exception during compilation
 672         lo = min_jlong;
 673         // do not support holes, 'hi' must go to either min_jlong or max_jlong:
 674         // [min_jlong, -10]/[-1,-1] ==> [min_jlong] UNION [10,max_jlong]
 675         hi = i1->_hi == min_jlong ? min_jlong : max_jlong;
 676       } else {
 677         lo = i1->_hi/d;
 678         hi = i1->_lo/d;
 679       }
 680     }
 681     return TypeLong::make(lo, hi, widen);
 682   }
 683 
 684   // If the dividend is a constant
 685   if( i1->is_con() ) {
 686     jlong d = i1->get_con();
 687     if( d < 0 ) {
 688       if( d == min_jlong ) {
 689         //  (-min_jlong) == min_jlong == (min_jlong / -1)
 690         return TypeLong::make(min_jlong, max_jlong/2 + 1, widen);
 691       } else {
 692         return TypeLong::make(d, -d, widen);
 693       }
 694     }
 695     return TypeLong::make(-d, d, widen);
 696   }
 697 
 698   // Otherwise we give up all hope
 699   return TypeLong::LONG;
 700 }
 701 
 702 
 703 //=============================================================================
 704 //------------------------------Value------------------------------------------
 705 // An DivFNode divides its inputs.  The third input is a Control input, used to
 706 // prevent hoisting the divide above an unsafe test.
 707 const Type* DivFNode::Value(PhaseGVN* phase) const {
 708   // Either input is TOP ==> the result is TOP
 709   const Type *t1 = phase->type( in(1) );
 710   const Type *t2 = phase->type( in(2) );
 711   if( t1 == Type::TOP ) return Type::TOP;
 712   if( t2 == Type::TOP ) return Type::TOP;
 713 
 714   // Either input is BOTTOM ==> the result is the local BOTTOM
 715   const Type *bot = bottom_type();
 716   if( (t1 == bot) || (t2 == bot) ||
 717       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 718     return bot;
 719 
 720   // x/x == 1, we ignore 0/0.
 721   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 722   // Does not work for variables because of NaN's
 723   if (in(1) == in(2) && t1->base() == Type::FloatCon &&
 724       !g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) { // could be negative ZERO or NaN
 725     return TypeF::ONE;
 726   }
 727 
 728   if( t2 == TypeF::ONE )
 729     return t1;
 730 
 731   // If divisor is a constant and not zero, divide them numbers
 732   if( t1->base() == Type::FloatCon &&
 733       t2->base() == Type::FloatCon &&
 734       t2->getf() != 0.0 ) // could be negative zero
 735     return TypeF::make( t1->getf()/t2->getf() );
 736 
 737   // If the dividend is a constant zero
 738   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 739   // Test TypeF::ZERO is not sufficient as it could be negative zero
 740 
 741   if( t1 == TypeF::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0 )
 742     return TypeF::ZERO;
 743 
 744   // Otherwise we give up all hope
 745   return Type::FLOAT;
 746 }
 747 
 748 //------------------------------isA_Copy---------------------------------------
 749 // Dividing by self is 1.
 750 // If the divisor is 1, we are an identity on the dividend.
 751 Node* DivFNode::Identity(PhaseGVN* phase) {
 752   return (phase->type( in(2) ) == TypeF::ONE) ? in(1) : this;
 753 }
 754 
 755 
 756 //------------------------------Idealize---------------------------------------
 757 Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 758   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 759   // Don't bother trying to transform a dead node
 760   if( in(0) && in(0)->is_top() )  return nullptr;
 761 
 762   const Type *t2 = phase->type( in(2) );
 763   if( t2 == TypeF::ONE )         // Identity?
 764     return nullptr;              // Skip it
 765 
 766   const TypeF *tf = t2->isa_float_constant();
 767   if( !tf ) return nullptr;
 768   if( tf->base() != Type::FloatCon ) return nullptr;
 769 
 770   // Check for out of range values
 771   if( tf->is_nan() || !tf->is_finite() ) return nullptr;
 772 
 773   // Get the value
 774   float f = tf->getf();
 775   int exp;
 776 
 777   // Only for special case of dividing by a power of 2
 778   if( frexp((double)f, &exp) != 0.5 ) return nullptr;
 779 
 780   // Limit the range of acceptable exponents
 781   if( exp < -126 || exp > 126 ) return nullptr;
 782 
 783   // Compute the reciprocal
 784   float reciprocal = ((float)1.0) / f;
 785 
 786   assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 787 
 788   // return multiplication by the reciprocal
 789   return (new MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
 790 }
 791 
 792 //=============================================================================
 793 //------------------------------Value------------------------------------------
 794 // An DivDNode divides its inputs.  The third input is a Control input, used to
 795 // prevent hoisting the divide above an unsafe test.
 796 const Type* DivDNode::Value(PhaseGVN* phase) const {
 797   // Either input is TOP ==> the result is TOP
 798   const Type *t1 = phase->type( in(1) );
 799   const Type *t2 = phase->type( in(2) );
 800   if( t1 == Type::TOP ) return Type::TOP;
 801   if( t2 == Type::TOP ) return Type::TOP;
 802 
 803   // Either input is BOTTOM ==> the result is the local BOTTOM
 804   const Type *bot = bottom_type();
 805   if( (t1 == bot) || (t2 == bot) ||
 806       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 807     return bot;
 808 
 809   // x/x == 1, we ignore 0/0.
 810   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 811   // Does not work for variables because of NaN's
 812   if (in(1) == in(2) && t1->base() == Type::DoubleCon &&
 813       !g_isnan(t1->getd()) && g_isfinite(t1->getd()) && t1->getd() != 0.0) { // could be negative ZERO or NaN
 814     return TypeD::ONE;
 815   }
 816 
 817   if( t2 == TypeD::ONE )
 818     return t1;
 819 
 820   // IA32 would only execute this for non-strict FP, which is never the
 821   // case now.
 822 #if ! defined(IA32)
 823   // If divisor is a constant and not zero, divide them numbers
 824   if( t1->base() == Type::DoubleCon &&
 825       t2->base() == Type::DoubleCon &&
 826       t2->getd() != 0.0 ) // could be negative zero
 827     return TypeD::make( t1->getd()/t2->getd() );
 828 #endif
 829 
 830   // If the dividend is a constant zero
 831   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 832   // Test TypeF::ZERO is not sufficient as it could be negative zero
 833   if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )
 834     return TypeD::ZERO;
 835 
 836   // Otherwise we give up all hope
 837   return Type::DOUBLE;
 838 }
 839 
 840 
 841 //------------------------------isA_Copy---------------------------------------
 842 // Dividing by self is 1.
 843 // If the divisor is 1, we are an identity on the dividend.
 844 Node* DivDNode::Identity(PhaseGVN* phase) {
 845   return (phase->type( in(2) ) == TypeD::ONE) ? in(1) : this;
 846 }
 847 
 848 //------------------------------Idealize---------------------------------------
 849 Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 850   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 851   // Don't bother trying to transform a dead node
 852   if( in(0) && in(0)->is_top() )  return nullptr;
 853 
 854   const Type *t2 = phase->type( in(2) );
 855   if( t2 == TypeD::ONE )         // Identity?
 856     return nullptr;              // Skip it
 857 
 858   const TypeD *td = t2->isa_double_constant();
 859   if( !td ) return nullptr;
 860   if( td->base() != Type::DoubleCon ) return nullptr;
 861 
 862   // Check for out of range values
 863   if( td->is_nan() || !td->is_finite() ) return nullptr;
 864 
 865   // Get the value
 866   double d = td->getd();
 867   int exp;
 868 
 869   // Only for special case of dividing by a power of 2
 870   if( frexp(d, &exp) != 0.5 ) return nullptr;
 871 
 872   // Limit the range of acceptable exponents
 873   if( exp < -1021 || exp > 1022 ) return nullptr;
 874 
 875   // Compute the reciprocal
 876   double reciprocal = 1.0 / d;
 877 
 878   assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 879 
 880   // return multiplication by the reciprocal
 881   return (new MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
 882 }
 883 
 884 //=============================================================================
 885 //------------------------------Identity---------------------------------------
 886 // If the divisor is 1, we are an identity on the dividend.
 887 Node* UDivINode::Identity(PhaseGVN* phase) {
 888   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
 889 }
 890 //------------------------------Value------------------------------------------
 891 // A UDivINode divides its inputs.  The third input is a Control input, used to
 892 // prevent hoisting the divide above an unsafe test.
 893 const Type* UDivINode::Value(PhaseGVN* phase) const {
 894   // Either input is TOP ==> the result is TOP
 895   const Type *t1 = phase->type( in(1) );
 896   const Type *t2 = phase->type( in(2) );
 897   if( t1 == Type::TOP ) return Type::TOP;
 898   if( t2 == Type::TOP ) return Type::TOP;
 899 
 900   // x/x == 1 since we always generate the dynamic divisor check for 0.
 901   if (in(1) == in(2)) {
 902     return TypeInt::ONE;
 903   }
 904 
 905   // Either input is BOTTOM ==> the result is the local BOTTOM
 906   const Type *bot = bottom_type();
 907   if( (t1 == bot) || (t2 == bot) ||
 908       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 909     return bot;
 910 
 911   // Otherwise we give up all hope
 912   return TypeInt::INT;
 913 }
 914 
 915 //------------------------------Idealize---------------------------------------
 916 Node *UDivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 917   return unsigned_div_ideal<TypeInt, juint>(phase, can_reshape, this);
 918 }
 919 
 920 //=============================================================================
 921 //------------------------------Identity---------------------------------------
 922 // If the divisor is 1, we are an identity on the dividend.
 923 Node* UDivLNode::Identity(PhaseGVN* phase) {
 924   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
 925 }
 926 //------------------------------Value------------------------------------------
 927 // A UDivLNode divides its inputs.  The third input is a Control input, used to
 928 // prevent hoisting the divide above an unsafe test.
 929 const Type* UDivLNode::Value(PhaseGVN* phase) const {
 930   // Either input is TOP ==> the result is TOP
 931   const Type *t1 = phase->type( in(1) );
 932   const Type *t2 = phase->type( in(2) );
 933   if( t1 == Type::TOP ) return Type::TOP;
 934   if( t2 == Type::TOP ) return Type::TOP;
 935 
 936   // x/x == 1 since we always generate the dynamic divisor check for 0.
 937   if (in(1) == in(2)) {
 938     return TypeLong::ONE;
 939   }
 940 
 941   // Either input is BOTTOM ==> the result is the local BOTTOM
 942   const Type *bot = bottom_type();
 943   if( (t1 == bot) || (t2 == bot) ||
 944       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 945     return bot;
 946 
 947   // Otherwise we give up all hope
 948   return TypeLong::LONG;
 949 }
 950 
 951 //------------------------------Idealize---------------------------------------
 952 Node *UDivLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 953   return unsigned_div_ideal<TypeLong, julong>(phase, can_reshape, this);
 954 }
 955 
 956 //=============================================================================
 957 //------------------------------Idealize---------------------------------------
 958 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 959   // Check for dead control input
 960   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
 961   // Don't bother trying to transform a dead node
 962   if( in(0) && in(0)->is_top() )  return nullptr;
 963 
 964   // Get the modulus
 965   const Type *t = phase->type( in(2) );
 966   if( t == Type::TOP ) return nullptr;
 967   const TypeInt *ti = t->is_int();
 968 
 969   // Check for useless control input
 970   // Check for excluding mod-zero case
 971   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
 972     set_req(0, nullptr);        // Yank control input
 973     return this;
 974   }
 975 
 976   // See if we are MOD'ing by 2^k or 2^k-1.
 977   if( !ti->is_con() ) return nullptr;
 978   jint con = ti->get_con();
 979 
 980   Node *hook = new Node(1);
 981 
 982   // First, special check for modulo 2^k-1
 983   if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
 984     uint k = exact_log2(con+1);  // Extract k
 985 
 986     // Basic algorithm by David Detlefs.  See fastmod_int.java for gory details.
 987     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*/};
 988     int trip_count = 1;
 989     if( k < ARRAY_SIZE(unroll_factor))  trip_count = unroll_factor[k];
 990 
 991     // If the unroll factor is not too large, and if conditional moves are
 992     // ok, then use this case
 993     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
 994       Node *x = in(1);            // Value being mod'd
 995       Node *divisor = in(2);      // Also is mask
 996 
 997       hook->init_req(0, x);       // Add a use to x to prevent him from dying
 998       // Generate code to reduce X rapidly to nearly 2^k-1.
 999       for( int i = 0; i < trip_count; i++ ) {
1000         Node *xl = phase->transform( new AndINode(x,divisor) );
1001         Node *xh = phase->transform( new RShiftINode(x,phase->intcon(k)) ); // Must be signed
1002         x = phase->transform( new AddINode(xh,xl) );
1003         hook->set_req(0, x);
1004       }
1005 
1006       // Generate sign-fixup code.  Was original value positive?
1007       // int hack_res = (i >= 0) ? divisor : 1;
1008       Node *cmp1 = phase->transform( new CmpINode( in(1), phase->intcon(0) ) );
1009       Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
1010       Node *cmov1= phase->transform( new CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
1011       // if( x >= hack_res ) x -= divisor;
1012       Node *sub  = phase->transform( new SubINode( x, divisor ) );
1013       Node *cmp2 = phase->transform( new CmpINode( x, cmov1 ) );
1014       Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
1015       // Convention is to not transform the return value of an Ideal
1016       // since Ideal is expected to return a modified 'this' or a new node.
1017       Node *cmov2= new CMoveINode(bol2, x, sub, TypeInt::INT);
1018       // cmov2 is now the mod
1019 
1020       // Now remove the bogus extra edges used to keep things alive
1021       hook->destruct(phase);
1022       return cmov2;
1023     }
1024   }
1025 
1026   // Fell thru, the unroll case is not appropriate. Transform the modulo
1027   // into a long multiply/int multiply/subtract case
1028 
1029   // Cannot handle mod 0, and min_jint isn't handled by the transform
1030   if( con == 0 || con == min_jint ) return nullptr;
1031 
1032   // Get the absolute value of the constant; at this point, we can use this
1033   jint pos_con = (con >= 0) ? con : -con;
1034 
1035   // integer Mod 1 is always 0
1036   if( pos_con == 1 ) return new ConINode(TypeInt::ZERO);
1037 
1038   int log2_con = -1;
1039 
1040   // If this is a power of two, they maybe we can mask it
1041   if (is_power_of_2(pos_con)) {
1042     log2_con = log2i_exact(pos_con);
1043 
1044     const Type *dt = phase->type(in(1));
1045     const TypeInt *dti = dt->isa_int();
1046 
1047     // See if this can be masked, if the dividend is non-negative
1048     if( dti && dti->_lo >= 0 )
1049       return ( new AndINode( in(1), phase->intcon( pos_con-1 ) ) );
1050   }
1051 
1052   // Save in(1) so that it cannot be changed or deleted
1053   hook->init_req(0, in(1));
1054 
1055   // Divide using the transform from DivI to MulL
1056   Node *result = transform_int_divide( phase, in(1), pos_con );
1057   if (result != nullptr) {
1058     Node *divide = phase->transform(result);
1059 
1060     // Re-multiply, using a shift if this is a power of two
1061     Node *mult = nullptr;
1062 
1063     if( log2_con >= 0 )
1064       mult = phase->transform( new LShiftINode( divide, phase->intcon( log2_con ) ) );
1065     else
1066       mult = phase->transform( new MulINode( divide, phase->intcon( pos_con ) ) );
1067 
1068     // Finally, subtract the multiplied divided value from the original
1069     result = new SubINode( in(1), mult );
1070   }
1071 
1072   // Now remove the bogus extra edges used to keep things alive
1073   hook->destruct(phase);
1074 
1075   // return the value
1076   return result;
1077 }
1078 
1079 //------------------------------Value------------------------------------------
1080 const Type* ModINode::Value(PhaseGVN* phase) const {
1081   // Either input is TOP ==> the result is TOP
1082   const Type *t1 = phase->type( in(1) );
1083   const Type *t2 = phase->type( in(2) );
1084   if( t1 == Type::TOP ) return Type::TOP;
1085   if( t2 == Type::TOP ) return Type::TOP;
1086 
1087   // We always generate the dynamic check for 0.
1088   // 0 MOD X is 0
1089   if( t1 == TypeInt::ZERO ) return TypeInt::ZERO;
1090   // X MOD X is 0
1091   if (in(1) == in(2)) {
1092     return TypeInt::ZERO;
1093   }
1094 
1095   // Either input is BOTTOM ==> the result is the local BOTTOM
1096   const Type *bot = bottom_type();
1097   if( (t1 == bot) || (t2 == bot) ||
1098       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1099     return bot;
1100 
1101   const TypeInt *i1 = t1->is_int();
1102   const TypeInt *i2 = t2->is_int();
1103   if( !i1->is_con() || !i2->is_con() ) {
1104     if( i1->_lo >= 0 && i2->_lo >= 0 )
1105       return TypeInt::POS;
1106     // If both numbers are not constants, we know little.
1107     return TypeInt::INT;
1108   }
1109   // Mod by zero?  Throw exception at runtime!
1110   if( !i2->get_con() ) return TypeInt::POS;
1111 
1112   // We must be modulo'ing 2 float constants.
1113   // Check for min_jint % '-1', result is defined to be '0'.
1114   if( i1->get_con() == min_jint && i2->get_con() == -1 )
1115     return TypeInt::ZERO;
1116 
1117   return TypeInt::make( i1->get_con() % i2->get_con() );
1118 }
1119 
1120 //=============================================================================
1121 //------------------------------Idealize---------------------------------------
1122 
1123 template <typename TypeClass, typename Unsigned>
1124 static Node* unsigned_mod_ideal(PhaseGVN* phase, bool can_reshape, Node* mod) {
1125   // Check for dead control input
1126   if (mod->in(0) != nullptr && mod->remove_dead_region(phase, can_reshape)) {
1127     return mod;
1128   }
1129   // Don't bother trying to transform a dead node
1130   if (mod->in(0) != nullptr && mod->in(0)->is_top()) {
1131     return nullptr;
1132   }
1133 
1134   // Get the modulus
1135   const Type* t = phase->type(mod->in(2));
1136   if (t == Type::TOP) {
1137     return nullptr;
1138   }
1139   const TypeClass* type_divisor = t->cast<TypeClass>();
1140 
1141   // Check for useless control input
1142   // Check for excluding mod-zero case
1143   if (mod->in(0) != nullptr && (type_divisor->_hi < 0 || type_divisor->_lo > 0)) {
1144     mod->set_req(0, nullptr); // Yank control input
1145     return mod;
1146   }
1147 
1148   if (!type_divisor->is_con()) {
1149     return nullptr;
1150   }
1151   Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con());
1152 
1153   if (divisor == 0) {
1154     return nullptr;
1155   }
1156 
1157   if (is_power_of_2(divisor)) {
1158     return make_and<TypeClass>(mod->in(1), phase->makecon(TypeClass::make(divisor - 1)));
1159   }
1160 
1161   return nullptr;
1162 }
1163 
1164 template <typename TypeClass, typename Unsigned, typename Signed>
1165 static const Type* unsigned_mod_value(PhaseGVN* phase, const Node* mod) {
1166   const Type* t1 = phase->type(mod->in(1));
1167   const Type* t2 = phase->type(mod->in(2));
1168   if (t1 == Type::TOP) {
1169     return Type::TOP;
1170   }
1171   if (t2 == Type::TOP) {
1172     return Type::TOP;
1173   }
1174 
1175   // 0 MOD X is 0
1176   if (t1 == TypeClass::ZERO) {
1177     return TypeClass::ZERO;
1178   }
1179   // X MOD X is 0
1180   if (mod->in(1) == mod->in(2)) {
1181     return TypeClass::ZERO;
1182   }
1183 
1184   // Either input is BOTTOM ==> the result is the local BOTTOM
1185   const Type* bot = mod->bottom_type();
1186   if ((t1 == bot) || (t2 == bot) ||
1187       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM)) {
1188     return bot;
1189   }
1190 
1191   const TypeClass* type_divisor = t2->cast<TypeClass>();
1192   if (type_divisor->is_con() && type_divisor->get_con() == 1) {
1193     return TypeClass::ZERO;
1194   }
1195 
1196   const TypeClass* type_dividend = t1->cast<TypeClass>();
1197   if (type_dividend->is_con() && type_divisor->is_con()) {
1198     Unsigned dividend = static_cast<Unsigned>(type_dividend->get_con());
1199     Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con());
1200     return TypeClass::make(static_cast<Signed>(dividend % divisor));
1201   }
1202 
1203   return bot;
1204 }
1205 
1206 Node* UModINode::Ideal(PhaseGVN* phase, bool can_reshape) {
1207   return unsigned_mod_ideal<TypeInt, juint>(phase, can_reshape, this);
1208 }
1209 
1210 const Type* UModINode::Value(PhaseGVN* phase) const {
1211   return unsigned_mod_value<TypeInt, juint, jint>(phase, this);
1212 }
1213 
1214 //=============================================================================
1215 //------------------------------Idealize---------------------------------------
1216 Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1217   // Check for dead control input
1218   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
1219   // Don't bother trying to transform a dead node
1220   if( in(0) && in(0)->is_top() )  return nullptr;
1221 
1222   // Get the modulus
1223   const Type *t = phase->type( in(2) );
1224   if( t == Type::TOP ) return nullptr;
1225   const TypeLong *tl = t->is_long();
1226 
1227   // Check for useless control input
1228   // Check for excluding mod-zero case
1229   if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
1230     set_req(0, nullptr);        // Yank control input
1231     return this;
1232   }
1233 
1234   // See if we are MOD'ing by 2^k or 2^k-1.
1235   if( !tl->is_con() ) return nullptr;
1236   jlong con = tl->get_con();
1237 
1238   Node *hook = new Node(1);
1239 
1240   // Expand mod
1241   if(con >= 0 && con < max_jlong && is_power_of_2(con + 1)) {
1242     uint k = log2i_exact(con + 1);  // Extract k
1243 
1244     // Basic algorithm by David Detlefs.  See fastmod_long.java for gory details.
1245     // Used to help a popular random number generator which does a long-mod
1246     // of 2^31-1 and shows up in SpecJBB and SciMark.
1247     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*/};
1248     int trip_count = 1;
1249     if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
1250 
1251     // If the unroll factor is not too large, and if conditional moves are
1252     // ok, then use this case
1253     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1254       Node *x = in(1);            // Value being mod'd
1255       Node *divisor = in(2);      // Also is mask
1256 
1257       hook->init_req(0, x);       // Add a use to x to prevent him from dying
1258       // Generate code to reduce X rapidly to nearly 2^k-1.
1259       for( int i = 0; i < trip_count; i++ ) {
1260         Node *xl = phase->transform( new AndLNode(x,divisor) );
1261         Node *xh = phase->transform( new RShiftLNode(x,phase->intcon(k)) ); // Must be signed
1262         x = phase->transform( new AddLNode(xh,xl) );
1263         hook->set_req(0, x);    // Add a use to x to prevent him from dying
1264       }
1265 
1266       // Generate sign-fixup code.  Was original value positive?
1267       // long hack_res = (i >= 0) ? divisor : CONST64(1);
1268       Node *cmp1 = phase->transform( new CmpLNode( in(1), phase->longcon(0) ) );
1269       Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
1270       Node *cmov1= phase->transform( new CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
1271       // if( x >= hack_res ) x -= divisor;
1272       Node *sub  = phase->transform( new SubLNode( x, divisor ) );
1273       Node *cmp2 = phase->transform( new CmpLNode( x, cmov1 ) );
1274       Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
1275       // Convention is to not transform the return value of an Ideal
1276       // since Ideal is expected to return a modified 'this' or a new node.
1277       Node *cmov2= new CMoveLNode(bol2, x, sub, TypeLong::LONG);
1278       // cmov2 is now the mod
1279 
1280       // Now remove the bogus extra edges used to keep things alive
1281       hook->destruct(phase);
1282       return cmov2;
1283     }
1284   }
1285 
1286   // Fell thru, the unroll case is not appropriate. Transform the modulo
1287   // into a long multiply/int multiply/subtract case
1288 
1289   // Cannot handle mod 0, and min_jlong isn't handled by the transform
1290   if( con == 0 || con == min_jlong ) return nullptr;
1291 
1292   // Get the absolute value of the constant; at this point, we can use this
1293   jlong pos_con = (con >= 0) ? con : -con;
1294 
1295   // integer Mod 1 is always 0
1296   if( pos_con == 1 ) return new ConLNode(TypeLong::ZERO);
1297 
1298   int log2_con = -1;
1299 
1300   // If this is a power of two, then maybe we can mask it
1301   if (is_power_of_2(pos_con)) {
1302     log2_con = log2i_exact(pos_con);
1303 
1304     const Type *dt = phase->type(in(1));
1305     const TypeLong *dtl = dt->isa_long();
1306 
1307     // See if this can be masked, if the dividend is non-negative
1308     if( dtl && dtl->_lo >= 0 )
1309       return ( new AndLNode( in(1), phase->longcon( pos_con-1 ) ) );
1310   }
1311 
1312   // Save in(1) so that it cannot be changed or deleted
1313   hook->init_req(0, in(1));
1314 
1315   // Divide using the transform from DivL to MulL
1316   Node *result = transform_long_divide( phase, in(1), pos_con );
1317   if (result != nullptr) {
1318     Node *divide = phase->transform(result);
1319 
1320     // Re-multiply, using a shift if this is a power of two
1321     Node *mult = nullptr;
1322 
1323     if( log2_con >= 0 )
1324       mult = phase->transform( new LShiftLNode( divide, phase->intcon( log2_con ) ) );
1325     else
1326       mult = phase->transform( new MulLNode( divide, phase->longcon( pos_con ) ) );
1327 
1328     // Finally, subtract the multiplied divided value from the original
1329     result = new SubLNode( in(1), mult );
1330   }
1331 
1332   // Now remove the bogus extra edges used to keep things alive
1333   hook->destruct(phase);
1334 
1335   // return the value
1336   return result;
1337 }
1338 
1339 //------------------------------Value------------------------------------------
1340 const Type* ModLNode::Value(PhaseGVN* phase) const {
1341   // Either input is TOP ==> the result is TOP
1342   const Type *t1 = phase->type( in(1) );
1343   const Type *t2 = phase->type( in(2) );
1344   if( t1 == Type::TOP ) return Type::TOP;
1345   if( t2 == Type::TOP ) return Type::TOP;
1346 
1347   // We always generate the dynamic check for 0.
1348   // 0 MOD X is 0
1349   if( t1 == TypeLong::ZERO ) return TypeLong::ZERO;
1350   // X MOD X is 0
1351   if (in(1) == in(2)) {
1352     return TypeLong::ZERO;
1353   }
1354 
1355   // Either input is BOTTOM ==> the result is the local BOTTOM
1356   const Type *bot = bottom_type();
1357   if( (t1 == bot) || (t2 == bot) ||
1358       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1359     return bot;
1360 
1361   const TypeLong *i1 = t1->is_long();
1362   const TypeLong *i2 = t2->is_long();
1363   if( !i1->is_con() || !i2->is_con() ) {
1364     if( i1->_lo >= CONST64(0) && i2->_lo >= CONST64(0) )
1365       return TypeLong::POS;
1366     // If both numbers are not constants, we know little.
1367     return TypeLong::LONG;
1368   }
1369   // Mod by zero?  Throw exception at runtime!
1370   if( !i2->get_con() ) return TypeLong::POS;
1371 
1372   // We must be modulo'ing 2 float constants.
1373   // Check for min_jint % '-1', result is defined to be '0'.
1374   if( i1->get_con() == min_jlong && i2->get_con() == -1 )
1375     return TypeLong::ZERO;
1376 
1377   return TypeLong::make( i1->get_con() % i2->get_con() );
1378 }
1379 
1380 
1381 //=============================================================================
1382 //------------------------------Value------------------------------------------
1383 const Type* ModFNode::Value(PhaseGVN* phase) const {
1384   // Either input is TOP ==> the result is TOP
1385   const Type *t1 = phase->type( in(1) );
1386   const Type *t2 = phase->type( in(2) );
1387   if( t1 == Type::TOP ) return Type::TOP;
1388   if( t2 == Type::TOP ) return Type::TOP;
1389 
1390   // Either input is BOTTOM ==> the result is the local BOTTOM
1391   const Type *bot = bottom_type();
1392   if( (t1 == bot) || (t2 == bot) ||
1393       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1394     return bot;
1395 
1396   // If either number is not a constant, we know nothing.
1397   if ((t1->base() != Type::FloatCon) || (t2->base() != Type::FloatCon)) {
1398     return Type::FLOAT;         // note: x%x can be either NaN or 0
1399   }
1400 
1401   float f1 = t1->getf();
1402   float f2 = t2->getf();
1403   jint  x1 = jint_cast(f1);     // note:  *(int*)&f1, not just (int)f1
1404   jint  x2 = jint_cast(f2);
1405 
1406   // If either is a NaN, return an input NaN
1407   if (g_isnan(f1))    return t1;
1408   if (g_isnan(f2))    return t2;
1409 
1410   // If an operand is infinity or the divisor is +/- zero, punt.
1411   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jint)
1412     return Type::FLOAT;
1413 
1414   // We must be modulo'ing 2 float constants.
1415   // Make sure that the sign of the fmod is equal to the sign of the dividend
1416   jint xr = jint_cast(fmod(f1, f2));
1417   if ((x1 ^ xr) < 0) {
1418     xr ^= min_jint;
1419   }
1420 
1421   return TypeF::make(jfloat_cast(xr));
1422 }
1423 
1424 //=============================================================================
1425 //------------------------------Idealize---------------------------------------
1426 Node *UModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1427   return unsigned_mod_ideal<TypeLong, julong>(phase, can_reshape, this);
1428 }
1429 
1430 const Type* UModLNode::Value(PhaseGVN* phase) const {
1431   return unsigned_mod_value<TypeLong, julong, jlong>(phase, this);
1432 }
1433 
1434 //=============================================================================
1435 //------------------------------Value------------------------------------------
1436 const Type* ModDNode::Value(PhaseGVN* phase) const {
1437   // Either input is TOP ==> the result is TOP
1438   const Type *t1 = phase->type( in(1) );
1439   const Type *t2 = phase->type( in(2) );
1440   if( t1 == Type::TOP ) return Type::TOP;
1441   if( t2 == Type::TOP ) return Type::TOP;
1442 
1443   // Either input is BOTTOM ==> the result is the local BOTTOM
1444   const Type *bot = bottom_type();
1445   if( (t1 == bot) || (t2 == bot) ||
1446       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1447     return bot;
1448 
1449   // If either number is not a constant, we know nothing.
1450   if ((t1->base() != Type::DoubleCon) || (t2->base() != Type::DoubleCon)) {
1451     return Type::DOUBLE;        // note: x%x can be either NaN or 0
1452   }
1453 
1454   double f1 = t1->getd();
1455   double f2 = t2->getd();
1456   jlong  x1 = jlong_cast(f1);   // note:  *(long*)&f1, not just (long)f1
1457   jlong  x2 = jlong_cast(f2);
1458 
1459   // If either is a NaN, return an input NaN
1460   if (g_isnan(f1))    return t1;
1461   if (g_isnan(f2))    return t2;
1462 
1463   // If an operand is infinity or the divisor is +/- zero, punt.
1464   if (!g_isfinite(f1) || !g_isfinite(f2) || x2 == 0 || x2 == min_jlong)
1465     return Type::DOUBLE;
1466 
1467   // We must be modulo'ing 2 double constants.
1468   // Make sure that the sign of the fmod is equal to the sign of the dividend
1469   jlong xr = jlong_cast(fmod(f1, f2));
1470   if ((x1 ^ xr) < 0) {
1471     xr ^= min_jlong;
1472   }
1473 
1474   return TypeD::make(jdouble_cast(xr));
1475 }
1476 
1477 //=============================================================================
1478 
1479 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
1480   init_req(0, c);
1481   init_req(1, dividend);
1482   init_req(2, divisor);
1483 }
1484 
1485 DivModNode* DivModNode::make(Node* div_or_mod, BasicType bt, bool is_unsigned) {
1486   assert(bt == T_INT || bt == T_LONG, "only int or long input pattern accepted");
1487 
1488   if (bt == T_INT) {
1489     if (is_unsigned) {
1490       return UDivModINode::make(div_or_mod);
1491     } else {
1492       return DivModINode::make(div_or_mod);
1493     }
1494   } else {
1495     if (is_unsigned) {
1496       return UDivModLNode::make(div_or_mod);
1497     } else {
1498       return DivModLNode::make(div_or_mod);
1499     }
1500   }
1501 }
1502 
1503 //------------------------------make------------------------------------------
1504 DivModINode* DivModINode::make(Node* div_or_mod) {
1505   Node* n = div_or_mod;
1506   assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
1507          "only div or mod input pattern accepted");
1508 
1509   DivModINode* divmod = new DivModINode(n->in(0), n->in(1), n->in(2));
1510   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1511   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1512   return divmod;
1513 }
1514 
1515 //------------------------------make------------------------------------------
1516 DivModLNode* DivModLNode::make(Node* div_or_mod) {
1517   Node* n = div_or_mod;
1518   assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
1519          "only div or mod input pattern accepted");
1520 
1521   DivModLNode* divmod = new DivModLNode(n->in(0), n->in(1), n->in(2));
1522   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1523   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1524   return divmod;
1525 }
1526 
1527 //------------------------------match------------------------------------------
1528 // return result(s) along with their RegMask info
1529 Node *DivModINode::match(const ProjNode *proj, const Matcher *match, const RegMask* mask) {
1530   uint ideal_reg = proj->ideal_reg();
1531   RegMask rm;
1532   if (proj->_con == div_proj_num) {
1533     rm = match->divI_proj_mask();
1534   } else {
1535     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1536     rm = match->modI_proj_mask();
1537   }
1538   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1539 }
1540 
1541 
1542 //------------------------------match------------------------------------------
1543 // return result(s) along with their RegMask info
1544 Node *DivModLNode::match(const ProjNode *proj, const Matcher *match, const RegMask* mask) {
1545   uint ideal_reg = proj->ideal_reg();
1546   RegMask rm;
1547   if (proj->_con == div_proj_num) {
1548     rm = match->divL_proj_mask();
1549   } else {
1550     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1551     rm = match->modL_proj_mask();
1552   }
1553   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1554 }
1555 
1556 //------------------------------make------------------------------------------
1557 UDivModINode* UDivModINode::make(Node* div_or_mod) {
1558   Node* n = div_or_mod;
1559   assert(n->Opcode() == Op_UDivI || n->Opcode() == Op_UModI,
1560          "only div or mod input pattern accepted");
1561 
1562   UDivModINode* divmod = new UDivModINode(n->in(0), n->in(1), n->in(2));
1563   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1564   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1565   return divmod;
1566 }
1567 
1568 //------------------------------make------------------------------------------
1569 UDivModLNode* UDivModLNode::make(Node* div_or_mod) {
1570   Node* n = div_or_mod;
1571   assert(n->Opcode() == Op_UDivL || n->Opcode() == Op_UModL,
1572          "only div or mod input pattern accepted");
1573 
1574   UDivModLNode* divmod = new UDivModLNode(n->in(0), n->in(1), n->in(2));
1575   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1576   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1577   return divmod;
1578 }
1579 
1580 //------------------------------match------------------------------------------
1581 // return result(s) along with their RegMask info
1582 Node* UDivModINode::match(const ProjNode* proj, const Matcher* match, const RegMask* mask) {
1583   uint ideal_reg = proj->ideal_reg();
1584   RegMask rm;
1585   if (proj->_con == div_proj_num) {
1586     rm = match->divI_proj_mask();
1587   } else {
1588     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1589     rm = match->modI_proj_mask();
1590   }
1591   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1592 }
1593 
1594 
1595 //------------------------------match------------------------------------------
1596 // return result(s) along with their RegMask info
1597 Node* UDivModLNode::match( const ProjNode* proj, const Matcher* match, const RegMask* mask) {
1598   uint ideal_reg = proj->ideal_reg();
1599   RegMask rm;
1600   if (proj->_con == div_proj_num) {
1601     rm = match->divL_proj_mask();
1602   } else {
1603     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1604     rm = match->modL_proj_mask();
1605   }
1606   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1607 }
--- EOF ---