1 /*
   2  * Copyright (c) 1997, 2026, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.
   8  *
   9  * This code is distributed in the hope that it will be useful, but WITHOUT
  10  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  11  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  12  * version 2 for more details (a copy is included in the LICENSE file that
  13  * accompanied this code).
  14  *
  15  * You should have received a copy of the GNU General Public License version
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  17  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  18  *
  19  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  20  * or visit www.oracle.com if you need additional information or have any
  21  * questions.
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  24 
  25 #include "memory/allocation.inline.hpp"
  26 #include "opto/addnode.hpp"
  27 #include "opto/connode.hpp"
  28 #include "opto/convertnode.hpp"
  29 #include "opto/divnode.hpp"
  30 #include "opto/machnode.hpp"
  31 #include "opto/matcher.hpp"
  32 #include "opto/movenode.hpp"
  33 #include "opto/mulnode.hpp"
  34 #include "opto/phaseX.hpp"
  35 #include "opto/runtime.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 ModFloatingNode::ModFloatingNode(Compile* C, const TypeFunc* tf, address addr, const char* name) : CallLeafPureNode(tf, addr, name) {
  46   add_flag(Flag_is_macro);
  47   C->add_macro_node(this);
  48 }
  49 
  50 ModDNode::ModDNode(Compile* C, Node* a, Node* b) : ModFloatingNode(C, OptoRuntime::Math_DD_D_Type(), CAST_FROM_FN_PTR(address, SharedRuntime::drem), "drem") {
  51   init_req(TypeFunc::Parms + 0, a);
  52   init_req(TypeFunc::Parms + 1, C->top());
  53   init_req(TypeFunc::Parms + 2, b);
  54   init_req(TypeFunc::Parms + 3, C->top());
  55 }
  56 
  57 ModFNode::ModFNode(Compile* C, Node* a, Node* b) : ModFloatingNode(C, OptoRuntime::modf_Type(), CAST_FROM_FN_PTR(address, SharedRuntime::frem), "frem") {
  58   init_req(TypeFunc::Parms + 0, a);
  59   init_req(TypeFunc::Parms + 1, b);
  60 }
  61 
  62 //----------------------magic_int_divide_constants-----------------------------
  63 // Compute magic multiplier and shift constant for converting a 32 bit divide
  64 // by constant into a multiply/shift/add series. Return false if calculations
  65 // fail.
  66 //
  67 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
  68 // minor type name and parameter changes.
  69 static bool magic_int_divide_constants(jint d, jint &M, jint &s) {
  70   int32_t p;
  71   uint32_t ad, anc, delta, q1, r1, q2, r2, t;
  72   const uint32_t two31 = 0x80000000L;     // 2**31.
  73 
  74   ad = ABS(d);
  75   if (d == 0 || d == 1) return false;
  76   t = two31 + ((uint32_t)d >> 31);
  77   anc = t - 1 - t%ad;     // Absolute value of nc.
  78   p = 31;                 // Init. p.
  79   q1 = two31/anc;         // Init. q1 = 2**p/|nc|.
  80   r1 = two31 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
  81   q2 = two31/ad;          // Init. q2 = 2**p/|d|.
  82   r2 = two31 - q2*ad;     // Init. r2 = rem(2**p, |d|).
  83   do {
  84     p = p + 1;
  85     q1 = 2*q1;            // Update q1 = 2**p/|nc|.
  86     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
  87     if (r1 >= anc) {      // (Must be an unsigned
  88       q1 = q1 + 1;        // comparison here).
  89       r1 = r1 - anc;
  90     }
  91     q2 = 2*q2;            // Update q2 = 2**p/|d|.
  92     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
  93     if (r2 >= ad) {       // (Must be an unsigned
  94       q2 = q2 + 1;        // comparison here).
  95       r2 = r2 - ad;
  96     }
  97     delta = ad - r2;
  98   } while (q1 < delta || (q1 == delta && r1 == 0));
  99 
 100   M = q2 + 1;
 101   if (d < 0) M = -M;      // Magic number and
 102   s = p - 32;             // shift amount to return.
 103 
 104   return true;
 105 }
 106 
 107 //--------------------------transform_int_divide-------------------------------
 108 // Convert a division by constant divisor into an alternate Ideal graph.
 109 // Return null if no transformation occurs.
 110 static Node *transform_int_divide( PhaseGVN *phase, Node *dividend, jint divisor ) {
 111 
 112   // Check for invalid divisors
 113   assert( divisor != 0 && divisor != min_jint,
 114           "bad divisor for transforming to long multiply" );
 115 
 116   bool d_pos = divisor >= 0;
 117   jint d = d_pos ? divisor : -divisor;
 118   const int N = 32;
 119 
 120   // Result
 121   Node *q = nullptr;
 122 
 123   if (d == 1) {
 124     // division by +/- 1
 125     if (!d_pos) {
 126       // Just negate the value
 127       q = new SubINode(phase->intcon(0), dividend);
 128     }
 129   } else if ( is_power_of_2(d) ) {
 130     // division by +/- a power of 2
 131 
 132     // See if we can simply do a shift without rounding
 133     bool needs_rounding = true;
 134     const Type *dt = phase->type(dividend);
 135     const TypeInt *dti = dt->isa_int();
 136     if (dti && dti->_lo >= 0) {
 137       // we don't need to round a positive dividend
 138       needs_rounding = false;
 139     } else if( dividend->Opcode() == Op_AndI ) {
 140       // An AND mask of sufficient size clears the low bits and
 141       // I can avoid rounding.
 142       const TypeInt *andconi_t = phase->type( dividend->in(2) )->isa_int();
 143       if( andconi_t && andconi_t->is_con() ) {
 144         jint andconi = andconi_t->get_con();
 145         if( andconi < 0 && is_power_of_2(-andconi) && (-andconi) >= d ) {
 146           if( (-andconi) == d ) // Remove AND if it clears bits which will be shifted
 147             dividend = dividend->in(1);
 148           needs_rounding = false;
 149         }
 150       }
 151     }
 152 
 153     // Add rounding to the shift to handle the sign bit
 154     int l = log2i_graceful(d - 1) + 1;
 155     if (needs_rounding) {
 156       // Divide-by-power-of-2 can be made into a shift, but you have to do
 157       // more math for the rounding.  You need to add 0 for positive
 158       // numbers, and "i-1" for negative numbers.  Example: i=4, so the
 159       // shift is by 2.  You need to add 3 to negative dividends and 0 to
 160       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
 161       // (-2+3)>>2 becomes 0, etc.
 162 
 163       // Compute 0 or -1, based on sign bit
 164       Node *sign = phase->transform(new RShiftINode(dividend, phase->intcon(N - 1)));
 165       // Mask sign bit to the low sign bits
 166       Node *round = phase->transform(new URShiftINode(sign, phase->intcon(N - l)));
 167       // Round up before shifting
 168       dividend = phase->transform(new AddINode(dividend, round));
 169     }
 170 
 171     // Shift for division
 172     q = new RShiftINode(dividend, phase->intcon(l));
 173 
 174     if (!d_pos) {
 175       q = new SubINode(phase->intcon(0), phase->transform(q));
 176     }
 177   } else {
 178     // Attempt the jint constant divide -> multiply transform found in
 179     //   "Division by Invariant Integers using Multiplication"
 180     //     by Granlund and Montgomery
 181     // See also "Hacker's Delight", chapter 10 by Warren.
 182 
 183     jint magic_const;
 184     jint shift_const;
 185     if (magic_int_divide_constants(d, magic_const, shift_const)) {
 186       Node *magic = phase->longcon(magic_const);
 187       Node *dividend_long = phase->transform(new ConvI2LNode(dividend));
 188 
 189       // Compute the high half of the dividend x magic multiplication
 190       Node *mul_hi = phase->transform(new MulLNode(dividend_long, magic));
 191 
 192       if (magic_const < 0) {
 193         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N)));
 194         mul_hi = phase->transform(new ConvL2INode(mul_hi));
 195 
 196         // The magic multiplier is too large for a 32 bit constant. We've adjusted
 197         // it down by 2^32, but have to add 1 dividend back in after the multiplication.
 198         // This handles the "overflow" case described by Granlund and Montgomery.
 199         mul_hi = phase->transform(new AddINode(dividend, mul_hi));
 200 
 201         // Shift over the (adjusted) mulhi
 202         if (shift_const != 0) {
 203           mul_hi = phase->transform(new RShiftINode(mul_hi, phase->intcon(shift_const)));
 204         }
 205       } else {
 206         // No add is required, we can merge the shifts together.
 207         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(N + shift_const)));
 208         mul_hi = phase->transform(new ConvL2INode(mul_hi));
 209       }
 210 
 211       // Get a 0 or -1 from the sign of the dividend.
 212       Node *addend0 = mul_hi;
 213       Node *addend1 = phase->transform(new RShiftINode(dividend, phase->intcon(N-1)));
 214 
 215       // If the divisor is negative, swap the order of the input addends;
 216       // this has the effect of negating the quotient.
 217       if (!d_pos) {
 218         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 219       }
 220 
 221       // Adjust the final quotient by subtracting -1 (adding 1)
 222       // from the mul_hi.
 223       q = new SubINode(addend0, addend1);
 224     }
 225   }
 226 
 227   return q;
 228 }
 229 
 230 //---------------------magic_long_divide_constants-----------------------------
 231 // Compute magic multiplier and shift constant for converting a 64 bit divide
 232 // by constant into a multiply/shift/add series. Return false if calculations
 233 // fail.
 234 //
 235 // Borrowed almost verbatim from Hacker's Delight by Henry S. Warren, Jr. with
 236 // minor type name and parameter changes.  Adjusted to 64 bit word width.
 237 static bool magic_long_divide_constants(jlong d, jlong &M, jint &s) {
 238   int64_t p;
 239   uint64_t ad, anc, delta, q1, r1, q2, r2, t;
 240   const uint64_t two63 = UCONST64(0x8000000000000000);     // 2**63.
 241 
 242   ad = ABS(d);
 243   if (d == 0 || d == 1) return false;
 244   t = two63 + ((uint64_t)d >> 63);
 245   anc = t - 1 - t%ad;     // Absolute value of nc.
 246   p = 63;                 // Init. p.
 247   q1 = two63/anc;         // Init. q1 = 2**p/|nc|.
 248   r1 = two63 - q1*anc;    // Init. r1 = rem(2**p, |nc|).
 249   q2 = two63/ad;          // Init. q2 = 2**p/|d|.
 250   r2 = two63 - q2*ad;     // Init. r2 = rem(2**p, |d|).
 251   do {
 252     p = p + 1;
 253     q1 = 2*q1;            // Update q1 = 2**p/|nc|.
 254     r1 = 2*r1;            // Update r1 = rem(2**p, |nc|).
 255     if (r1 >= anc) {      // (Must be an unsigned
 256       q1 = q1 + 1;        // comparison here).
 257       r1 = r1 - anc;
 258     }
 259     q2 = 2*q2;            // Update q2 = 2**p/|d|.
 260     r2 = 2*r2;            // Update r2 = rem(2**p, |d|).
 261     if (r2 >= ad) {       // (Must be an unsigned
 262       q2 = q2 + 1;        // comparison here).
 263       r2 = r2 - ad;
 264     }
 265     delta = ad - r2;
 266   } while (q1 < delta || (q1 == delta && r1 == 0));
 267 
 268   M = q2 + 1;
 269   if (d < 0) M = -M;      // Magic number and
 270   s = p - 64;             // shift amount to return.
 271 
 272   return true;
 273 }
 274 
 275 //---------------------long_by_long_mulhi--------------------------------------
 276 // Generate ideal node graph for upper half of a 64 bit x 64 bit multiplication
 277 static Node* long_by_long_mulhi(PhaseGVN* phase, Node* dividend, jlong magic_const) {
 278   // If the architecture supports a 64x64 mulhi, there is
 279   // no need to synthesize it in ideal nodes.
 280   if (Matcher::has_match_rule(Op_MulHiL)) {
 281     Node* v = phase->longcon(magic_const);
 282     return new MulHiLNode(dividend, v);
 283   }
 284 
 285   // Taken from Hacker's Delight, Fig. 8-2. Multiply high signed.
 286   //
 287   // int mulhs(int u, int v) {
 288   //    unsigned u0, v0, w0;
 289   //    int u1, v1, w1, w2, t;
 290   //
 291   //    u0 = u & 0xFFFF;  u1 = u >> 16;
 292   //    v0 = v & 0xFFFF;  v1 = v >> 16;
 293   //    w0 = u0*v0;
 294   //    t  = u1*v0 + (w0 >> 16);
 295   //    w1 = t & 0xFFFF;
 296   //    w2 = t >> 16;
 297   //    w1 = u0*v1 + w1;
 298   //    return u1*v1 + w2 + (w1 >> 16);
 299   // }
 300   //
 301   // Note: The version above is for 32x32 multiplications, while the
 302   // following inline comments are adapted to 64x64.
 303 
 304   const int N = 64;
 305 
 306   // Dummy node to keep intermediate nodes alive during construction
 307   Node* hook = new Node(4);
 308 
 309   // u0 = u & 0xFFFFFFFF;  u1 = u >> 32;
 310   Node* u0 = phase->transform(new AndLNode(dividend, phase->longcon(0xFFFFFFFF)));
 311   Node* u1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N / 2)));
 312   hook->init_req(0, u0);
 313   hook->init_req(1, u1);
 314 
 315   // v0 = v & 0xFFFFFFFF;  v1 = v >> 32;
 316   Node* v0 = phase->longcon(magic_const & 0xFFFFFFFF);
 317   Node* v1 = phase->longcon(magic_const >> (N / 2));
 318 
 319   // w0 = u0*v0;
 320   Node* w0 = phase->transform(new MulLNode(u0, v0));
 321 
 322   // t = u1*v0 + (w0 >> 32);
 323   Node* u1v0 = phase->transform(new MulLNode(u1, v0));
 324   Node* temp = phase->transform(new URShiftLNode(w0, phase->intcon(N / 2)));
 325   Node* t    = phase->transform(new AddLNode(u1v0, temp));
 326   hook->init_req(2, t);
 327 
 328   // w1 = t & 0xFFFFFFFF;
 329   Node* w1 = phase->transform(new AndLNode(t, phase->longcon(0xFFFFFFFF)));
 330   hook->init_req(3, w1);
 331 
 332   // w2 = t >> 32;
 333   Node* w2 = phase->transform(new RShiftLNode(t, phase->intcon(N / 2)));
 334 
 335   // w1 = u0*v1 + w1;
 336   Node* u0v1 = phase->transform(new MulLNode(u0, v1));
 337   w1         = phase->transform(new AddLNode(u0v1, w1));
 338 
 339   // return u1*v1 + w2 + (w1 >> 32);
 340   Node* u1v1  = phase->transform(new MulLNode(u1, v1));
 341   Node* temp1 = phase->transform(new AddLNode(u1v1, w2));
 342   Node* temp2 = phase->transform(new RShiftLNode(w1, phase->intcon(N / 2)));
 343 
 344   // Remove the bogus extra edges used to keep things alive
 345   hook->destruct(phase);
 346 
 347   return new AddLNode(temp1, temp2);
 348 }
 349 
 350 
 351 //--------------------------transform_long_divide------------------------------
 352 // Convert a division by constant divisor into an alternate Ideal graph.
 353 // Return null if no transformation occurs.
 354 static Node *transform_long_divide( PhaseGVN *phase, Node *dividend, jlong divisor ) {
 355   // Check for invalid divisors
 356   assert( divisor != 0L && divisor != min_jlong,
 357           "bad divisor for transforming to long multiply" );
 358 
 359   bool d_pos = divisor >= 0;
 360   jlong d = d_pos ? divisor : -divisor;
 361   const int N = 64;
 362 
 363   // Result
 364   Node *q = nullptr;
 365 
 366   if (d == 1) {
 367     // division by +/- 1
 368     if (!d_pos) {
 369       // Just negate the value
 370       q = new SubLNode(phase->longcon(0), dividend);
 371     }
 372   } else if ( is_power_of_2(d) ) {
 373 
 374     // division by +/- a power of 2
 375 
 376     // See if we can simply do a shift without rounding
 377     bool needs_rounding = true;
 378     const Type *dt = phase->type(dividend);
 379     const TypeLong *dtl = dt->isa_long();
 380 
 381     if (dtl && dtl->_lo > 0) {
 382       // we don't need to round a positive dividend
 383       needs_rounding = false;
 384     } else if( dividend->Opcode() == Op_AndL ) {
 385       // An AND mask of sufficient size clears the low bits and
 386       // I can avoid rounding.
 387       const TypeLong *andconl_t = phase->type( dividend->in(2) )->isa_long();
 388       if( andconl_t && andconl_t->is_con() ) {
 389         jlong andconl = andconl_t->get_con();
 390         if( andconl < 0 && is_power_of_2(-andconl) && (-andconl) >= d ) {
 391           if( (-andconl) == d ) // Remove AND if it clears bits which will be shifted
 392             dividend = dividend->in(1);
 393           needs_rounding = false;
 394         }
 395       }
 396     }
 397 
 398     // Add rounding to the shift to handle the sign bit
 399     int l = log2i_graceful(d - 1) + 1;
 400     if (needs_rounding) {
 401       // Divide-by-power-of-2 can be made into a shift, but you have to do
 402       // more math for the rounding.  You need to add 0 for positive
 403       // numbers, and "i-1" for negative numbers.  Example: i=4, so the
 404       // shift is by 2.  You need to add 3 to negative dividends and 0 to
 405       // positive ones.  So (-7+3)>>2 becomes -1, (-4+3)>>2 becomes -1,
 406       // (-2+3)>>2 becomes 0, etc.
 407 
 408       // Compute 0 or -1, based on sign bit
 409       Node *sign = phase->transform(new RShiftLNode(dividend, phase->intcon(N - 1)));
 410       // Mask sign bit to the low sign bits
 411       Node *round = phase->transform(new URShiftLNode(sign, phase->intcon(N - l)));
 412       // Round up before shifting
 413       dividend = phase->transform(new AddLNode(dividend, round));
 414     }
 415 
 416     // Shift for division
 417     q = new RShiftLNode(dividend, phase->intcon(l));
 418 
 419     if (!d_pos) {
 420       q = new SubLNode(phase->longcon(0), phase->transform(q));
 421     }
 422   } else {
 423     // Attempt the jlong constant divide -> multiply transform found in
 424     //   "Division by Invariant Integers using Multiplication"
 425     //     by Granlund and Montgomery
 426     // See also "Hacker's Delight", chapter 10 by Warren.
 427 
 428     jlong magic_const;
 429     jint shift_const;
 430     if (magic_long_divide_constants(d, magic_const, shift_const)) {
 431       // Compute the high half of the dividend x magic multiplication
 432       Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
 433 
 434       // The high half of the 128-bit multiply is computed.
 435       if (magic_const < 0) {
 436         // The magic multiplier is too large for a 64 bit constant. We've adjusted
 437         // it down by 2^64, but have to add 1 dividend back in after the multiplication.
 438         // This handles the "overflow" case described by Granlund and Montgomery.
 439         mul_hi = phase->transform(new AddLNode(dividend, mul_hi));
 440       }
 441 
 442       // Shift over the (adjusted) mulhi
 443       if (shift_const != 0) {
 444         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(shift_const)));
 445       }
 446 
 447       // Get a 0 or -1 from the sign of the dividend.
 448       Node *addend0 = mul_hi;
 449       Node *addend1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N-1)));
 450 
 451       // If the divisor is negative, swap the order of the input addends;
 452       // this has the effect of negating the quotient.
 453       if (!d_pos) {
 454         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 455       }
 456 
 457       // Adjust the final quotient by subtracting -1 (adding 1)
 458       // from the mul_hi.
 459       q = new SubLNode(addend0, addend1);
 460     }
 461   }
 462 
 463   return q;
 464 }
 465 
 466 template <typename TypeClass, typename Unsigned>
 467 Node* unsigned_div_ideal(PhaseGVN* phase, bool can_reshape, Node* div) {
 468   // Check for dead control input
 469   if (div->in(0) != nullptr && div->remove_dead_region(phase, can_reshape)) {
 470     return div;
 471   }
 472   // Don't bother trying to transform a dead node
 473   if (div->in(0) != nullptr && div->in(0)->is_top()) {
 474     return nullptr;
 475   }
 476 
 477   const Type* t = phase->type(div->in(2));
 478   if (t == Type::TOP) {
 479     return nullptr;
 480   }
 481   const TypeClass* type_divisor = t->cast<TypeClass>();
 482 
 483   // Check for useless control input
 484   // Check for excluding div-zero case
 485   if (div->in(0) != nullptr && (type_divisor->_hi < 0 || type_divisor->_lo > 0)) {
 486     div->set_req(0, nullptr); // Yank control input
 487     return div;
 488   }
 489 
 490   if (!type_divisor->is_con()) {
 491     return nullptr;
 492   }
 493   Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con()); // Get divisor
 494 
 495   if (divisor == 0 || divisor == 1) {
 496     return nullptr; // Dividing by zero constant does not idealize
 497   }
 498 
 499   if (is_power_of_2(divisor)) {
 500     return make_urshift<TypeClass>(div->in(1), phase->intcon(log2i_graceful(divisor)));
 501   }
 502 
 503   return nullptr;
 504 }
 505 
 506 template<typename IntegerType>
 507 static const IntegerType* compute_signed_div_type(const IntegerType* i1, const IntegerType* i2) {
 508   typedef typename IntegerType::NativeType NativeType;
 509   assert(!i2->is_con() || i2->get_con() != 0, "Can't handle zero constant divisor");
 510   int widen = MAX2(i1->_widen, i2->_widen);
 511 
 512   // Case A: divisor range spans zero (i2->_lo < 0 < i2->_hi)
 513   // We split into two subproblems to avoid division by 0:
 514   //   - negative part: [i2->_lo, −1]
 515   //   - positive part: [1, i2->_hi]
 516   // Then we union the results by taking the min of all lower‐bounds and
 517   // the max of all upper‐bounds from the two halves.
 518   if (i2->_lo < 0 && i2->_hi > 0) {
 519     // Handle negative part of the divisor range
 520     const IntegerType* neg_part = compute_signed_div_type(i1, IntegerType::make(i2->_lo, -1, widen));
 521     // Handle positive part of the divisor range
 522     const IntegerType* pos_part = compute_signed_div_type(i1, IntegerType::make(1, i2->_hi, widen));
 523     // Merge results
 524     NativeType new_lo = MIN2(neg_part->_lo, pos_part->_lo);
 525     NativeType new_hi = MAX2(neg_part->_hi, pos_part->_hi);
 526     assert(new_hi >= new_lo, "sanity");
 527     return IntegerType::make(new_lo, new_hi, widen);
 528   }
 529 
 530   // Case B: divisor range does NOT span zero.
 531   // Here i2 is entirely negative or entirely positive.
 532   // Then i1/i2 is monotonic in i1 and i2 (when i2 keeps the same sign).
 533   // Therefore the extrema occur at the four “corners”:
 534   //   (i1->_lo, i2->_hi), (i1->_lo, i2->_lo), (i1->_hi, i2->_lo), (i1->_hi, i2->_hi).
 535   // We compute all four and take the min and max.
 536   // A special case handles overflow when dividing the most‐negative value by −1.
 537 
 538   // adjust i2 bounds to not include zero, as zero always throws
 539   NativeType i2_lo = i2->_lo == 0 ? 1 : i2->_lo;
 540   NativeType i2_hi = i2->_hi == 0 ? -1 : i2->_hi;
 541   constexpr NativeType min_val = std::numeric_limits<NativeType>::min();
 542   static_assert(min_val == min_jint || min_val == min_jlong, "min has to be either min_jint or min_jlong");
 543   constexpr NativeType max_val = std::numeric_limits<NativeType>::max();
 544   static_assert(max_val == max_jint || max_val == max_jlong, "max has to be either max_jint or max_jlong");
 545 
 546   // Special overflow case: min_val / (-1) == min_val (cf. JVMS§6.5 idiv/ldiv)
 547   // We need to be careful that we never run min_val / (-1) in C++ code, as this overflow is UB there
 548   if (i1->_lo == min_val && i2_hi == -1) {
 549     NativeType new_lo = min_val;
 550     NativeType new_hi;
 551     // compute new_hi depending on whether divisor or dividend is non-constant.
 552     // i2 is purely in the negative domain here (as i2_hi is -1)
 553     // which means the maximum value this division can yield is either
 554     if (!i1->is_con()) {
 555       // a) non-constant dividend: i1 could be min_val + 1.
 556       // -> i1 / i2 = (min_val + 1) / -1 = max_val is possible.
 557       new_hi = max_val;
 558       assert((min_val + 1) / -1 == new_hi, "new_hi should be max_val");
 559     } else if (i2_lo != i2_hi) {
 560       // b) i1 is constant min_val, i2 is non-constant.
 561       //    if i2 = -1 -> i1 / i2 =  min_val / -1 = min_val
 562       //    if i2 < -1 -> i1 / i2 <= min_val / -2 = (max_val / 2) + 1
 563       new_hi = (max_val / 2) + 1;
 564       assert(min_val / -2 == new_hi, "new_hi should be (max_val / 2) + 1)");
 565     } else {
 566       // c) i1 is constant min_val, i2 is constant -1.
 567       //    -> i1 / i2 = min_val / -1 = min_val
 568       new_hi = min_val;
 569     }
 570 
 571 #ifdef ASSERT
 572     // validate new_hi for non-constant divisor
 573     if (i2_lo != i2_hi) {
 574       assert(i2_lo != -1, "Special case not possible here, as i2_lo has to be < i2_hi");
 575       NativeType result = i1->_lo / i2_lo;
 576       assert(new_hi >= result, "computed wrong value for new_hi");
 577     }
 578 
 579     // validate new_hi for non-constant dividend
 580     if (!i1->is_con()) {
 581       assert(i2_hi > min_val, "Special case not possible here, as i1->_hi has to be > min");
 582       NativeType result1 = i1->_hi / i2_lo;
 583       NativeType result2 = i1->_hi / i2_hi;
 584       assert(new_hi >= result1 && new_hi >= result2, "computed wrong value for new_hi");
 585     }
 586 #endif
 587 
 588     return IntegerType::make(new_lo, new_hi, widen);
 589   }
 590   assert((i1->_lo != min_val && i1->_hi != min_val) || (i2_hi != -1 && i2_lo != -1), "should have filtered out before");
 591 
 592   // Special case not possible here, calculate all corners normally
 593   NativeType corner1 = i1->_lo / i2_lo;
 594   NativeType corner2 = i1->_lo / i2_hi;
 595   NativeType corner3 = i1->_hi / i2_lo;
 596   NativeType corner4 = i1->_hi / i2_hi;
 597 
 598   NativeType new_lo = MIN4(corner1, corner2, corner3, corner4);
 599   NativeType new_hi = MAX4(corner1, corner2, corner3, corner4);
 600   return IntegerType::make(new_lo, new_hi, widen);
 601 }
 602 
 603 //=============================================================================
 604 //------------------------------Identity---------------------------------------
 605 // If the divisor is 1, we are an identity on the dividend.
 606 Node* DivINode::Identity(PhaseGVN* phase) {
 607   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
 608 }
 609 
 610 //------------------------------Idealize---------------------------------------
 611 // Divides can be changed to multiplies and/or shifts
 612 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 613   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 614   // Don't bother trying to transform a dead node
 615   if( in(0) && in(0)->is_top() )  return nullptr;
 616 
 617   const Type *t = phase->type( in(2) );
 618   if( t == TypeInt::ONE )      // Identity?
 619     return nullptr;            // Skip it
 620 
 621   const TypeInt *ti = t->isa_int();
 622   if( !ti ) return nullptr;
 623 
 624   // Check for useless control input
 625   // Check for excluding div-zero case
 626   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
 627     set_req(0, nullptr);           // Yank control input
 628     return this;
 629   }
 630 
 631   if( !ti->is_con() ) return nullptr;
 632   jint i = ti->get_con();       // Get divisor
 633 
 634   if (i == 0) return nullptr;   // Dividing by zero constant does not idealize
 635 
 636   // Dividing by MININT does not optimize as a power-of-2 shift.
 637   if( i == min_jint ) return nullptr;
 638 
 639   return transform_int_divide( phase, in(1), i );
 640 }
 641 
 642 //------------------------------Value------------------------------------------
 643 // A DivINode divides its inputs.  The third input is a Control input, used to
 644 // prevent hoisting the divide above an unsafe test.
 645 const Type* DivINode::Value(PhaseGVN* phase) const {
 646   // Either input is TOP ==> the result is TOP
 647   const Type* t1 = phase->type(in(1));
 648   const Type* t2 = phase->type(in(2));
 649   if (t1 == Type::TOP || t2 == Type::TOP) {
 650     return Type::TOP;
 651   }
 652 
 653   if (t2 == TypeInt::ZERO) {
 654     // this division will always throw an exception
 655     return Type::TOP;
 656   }
 657 
 658   // x/x == 1 since we always generate the dynamic divisor check for 0.
 659   if (in(1) == in(2)) {
 660     return TypeInt::ONE;
 661   }
 662 
 663   const TypeInt* i1 = t1->is_int();
 664   const TypeInt* i2 = t2->is_int();
 665 
 666   return compute_signed_div_type<TypeInt>(i1, i2);
 667 }
 668 
 669 
 670 //=============================================================================
 671 //------------------------------Identity---------------------------------------
 672 // If the divisor is 1, we are an identity on the dividend.
 673 Node* DivLNode::Identity(PhaseGVN* phase) {
 674   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
 675 }
 676 
 677 //------------------------------Idealize---------------------------------------
 678 // Dividing by a power of 2 is a shift.
 679 Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) {
 680   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 681   // Don't bother trying to transform a dead node
 682   if( in(0) && in(0)->is_top() )  return nullptr;
 683 
 684   const Type *t = phase->type( in(2) );
 685   if( t == TypeLong::ONE )      // Identity?
 686     return nullptr;             // Skip it
 687 
 688   const TypeLong *tl = t->isa_long();
 689   if( !tl ) return nullptr;
 690 
 691   // Check for useless control input
 692   // Check for excluding div-zero case
 693   if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
 694     set_req(0, nullptr);         // Yank control input
 695     return this;
 696   }
 697 
 698   if( !tl->is_con() ) return nullptr;
 699   jlong l = tl->get_con();      // Get divisor
 700 
 701   if (l == 0) return nullptr;   // Dividing by zero constant does not idealize
 702 
 703   // Dividing by MINLONG does not optimize as a power-of-2 shift.
 704   if( l == min_jlong ) return nullptr;
 705 
 706   return transform_long_divide( phase, in(1), l );
 707 }
 708 
 709 //------------------------------Value------------------------------------------
 710 // A DivLNode divides its inputs.  The third input is a Control input, used to
 711 // prevent hoisting the divide above an unsafe test.
 712 const Type* DivLNode::Value(PhaseGVN* phase) const {
 713   // Either input is TOP ==> the result is TOP
 714   const Type* t1 = phase->type(in(1));
 715   const Type* t2 = phase->type(in(2));
 716   if (t1 == Type::TOP || t2 == Type::TOP) {
 717     return Type::TOP;
 718   }
 719 
 720   if (t2 == TypeLong::ZERO) {
 721     // this division will always throw an exception
 722     return Type::TOP;
 723   }
 724 
 725   // x/x == 1 since we always generate the dynamic divisor check for 0.
 726   if (in(1) == in(2)) {
 727     return TypeLong::ONE;
 728   }
 729 
 730   const TypeLong* i1 = t1->is_long();
 731   const TypeLong* i2 = t2->is_long();
 732 
 733   return compute_signed_div_type<TypeLong>(i1, i2);
 734 }
 735 
 736 
 737 //=============================================================================
 738 //------------------------------Value------------------------------------------
 739 // An DivFNode divides its inputs.  The third input is a Control input, used to
 740 // prevent hoisting the divide above an unsafe test.
 741 const Type* DivFNode::Value(PhaseGVN* phase) const {
 742   // Either input is TOP ==> the result is TOP
 743   const Type *t1 = phase->type( in(1) );
 744   const Type *t2 = phase->type( in(2) );
 745   if( t1 == Type::TOP ) return Type::TOP;
 746   if( t2 == Type::TOP ) return Type::TOP;
 747 
 748   // Either input is BOTTOM ==> the result is the local BOTTOM
 749   const Type *bot = bottom_type();
 750   if( (t1 == bot) || (t2 == bot) ||
 751       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 752     return bot;
 753 
 754   // x/x == 1, we ignore 0/0.
 755   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 756   // Does not work for variables because of NaN's
 757   if (in(1) == in(2) && t1->base() == Type::FloatCon &&
 758       !g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) { // could be negative ZERO or NaN
 759     return TypeF::ONE;
 760   }
 761 
 762   if( t2 == TypeF::ONE )
 763     return t1;
 764 
 765   // If divisor is a constant and not zero, divide them numbers
 766   if( t1->base() == Type::FloatCon &&
 767       t2->base() == Type::FloatCon &&
 768       t2->getf() != 0.0 ) // could be negative zero
 769     return TypeF::make( t1->getf()/t2->getf() );
 770 
 771   // If the dividend is a constant zero
 772   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 773   // Test TypeF::ZERO is not sufficient as it could be negative zero
 774 
 775   if( t1 == TypeF::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0 )
 776     return TypeF::ZERO;
 777 
 778   // Otherwise we give up all hope
 779   return Type::FLOAT;
 780 }
 781 
 782 //------------------------------isA_Copy---------------------------------------
 783 // Dividing by self is 1.
 784 // If the divisor is 1, we are an identity on the dividend.
 785 Node* DivFNode::Identity(PhaseGVN* phase) {
 786   return (phase->type( in(2) ) == TypeF::ONE) ? in(1) : this;
 787 }
 788 
 789 
 790 //------------------------------Idealize---------------------------------------
 791 Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 792   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 793   // Don't bother trying to transform a dead node
 794   if( in(0) && in(0)->is_top() )  return nullptr;
 795 
 796   const Type *t2 = phase->type( in(2) );
 797   if( t2 == TypeF::ONE )         // Identity?
 798     return nullptr;              // Skip it
 799 
 800   const TypeF *tf = t2->isa_float_constant();
 801   if( !tf ) return nullptr;
 802   if( tf->base() != Type::FloatCon ) return nullptr;
 803 
 804   // Check for out of range values
 805   if( tf->is_nan() || !tf->is_finite() ) return nullptr;
 806 
 807   // Get the value
 808   float f = tf->getf();
 809   int exp;
 810 
 811   // Only for special case of dividing by a power of 2
 812   if( frexp((double)f, &exp) != 0.5 ) return nullptr;
 813 
 814   // Limit the range of acceptable exponents
 815   if( exp < -126 || exp > 126 ) return nullptr;
 816 
 817   // Compute the reciprocal
 818   float reciprocal = ((float)1.0) / f;
 819 
 820   assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 821 
 822   // return multiplication by the reciprocal
 823   return (new MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
 824 }
 825 //=============================================================================
 826 //------------------------------Value------------------------------------------
 827 // An DivHFNode divides its inputs.  The third input is a Control input, used to
 828 // prevent hoisting the divide above an unsafe test.
 829 const Type* DivHFNode::Value(PhaseGVN* phase) const {
 830   // Either input is TOP ==> the result is TOP
 831   const Type* t1 = phase->type(in(1));
 832   const Type* t2 = phase->type(in(2));
 833   if(t1 == Type::TOP) { return Type::TOP; }
 834   if(t2 == Type::TOP) { return Type::TOP; }
 835 
 836   // Either input is BOTTOM ==> the result is the local BOTTOM
 837   const Type* bot = bottom_type();
 838   if((t1 == bot) || (t2 == bot) ||
 839      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM)) {
 840     return bot;
 841   }
 842 
 843   if (t1->base() == Type::HalfFloatCon &&
 844       t2->base() == Type::HalfFloatCon)  {
 845     // IEEE 754 floating point comparison treats 0.0 and -0.0 as equals.
 846 
 847     // Division of a zero by a zero results in NaN.
 848     if (t1->getf() == 0.0f && t2->getf() == 0.0f) {
 849       return TypeH::make(NAN);
 850     }
 851 
 852     // As per C++ standard section 7.6.5 (expr.mul), behavior is undefined only if
 853     // the second operand is 0.0. In all other situations, we can expect a standard-compliant
 854     // C++ compiler to generate code following IEEE 754 semantics.
 855     if (t2->getf() == 0.0) {
 856       // If either operand is NaN, the result is NaN
 857       if (g_isnan(t1->getf())) {
 858         return TypeH::make(NAN);
 859       } else {
 860         // Division of a nonzero finite value by a zero results in a signed infinity. Also,
 861         // division of an infinity by a finite value results in a signed infinity.
 862         bool res_sign_neg = (jint_cast(t1->getf()) < 0) ^ (jint_cast(t2->getf()) < 0);
 863         const TypeF* res = res_sign_neg ? TypeF::NEG_INF : TypeF::POS_INF;
 864         return TypeH::make(res->getf());
 865       }
 866     }
 867 
 868     return TypeH::make(t1->getf() / t2->getf());
 869   }
 870 
 871   // Otherwise we give up all hope
 872   return Type::HALF_FLOAT;
 873 }
 874 
 875 //-----------------------------------------------------------------------------
 876 // Dividing by self is 1.
 877 // IF the divisor is 1, we are an identity on the dividend.
 878 Node* DivHFNode::Identity(PhaseGVN* phase) {
 879   return (phase->type( in(2) ) == TypeH::ONE) ? in(1) : this;
 880 }
 881 
 882 
 883 //------------------------------Idealize---------------------------------------
 884 Node* DivHFNode::Ideal(PhaseGVN* phase, bool can_reshape) {
 885   if (in(0) != nullptr && remove_dead_region(phase, can_reshape))  return this;
 886   // Don't bother trying to transform a dead node
 887   if (in(0) != nullptr && in(0)->is_top())  { return nullptr; }
 888 
 889   const Type* t2 = phase->type(in(2));
 890   if (t2 == TypeH::ONE) {      // Identity?
 891     return nullptr;            // Skip it
 892   }
 893   const TypeH* tf = t2->isa_half_float_constant();
 894   if(tf == nullptr) { return nullptr; }
 895   if(tf->base() != Type::HalfFloatCon) { return nullptr; }
 896 
 897   // Check for out of range values
 898   if(tf->is_nan() || !tf->is_finite()) { return nullptr; }
 899 
 900   // Get the value
 901   float f = tf->getf();
 902   int exp;
 903 
 904   // Consider the following geometric progression series of POT(power of two) numbers.
 905   // 0.5 x 2^0 = 0.5, 0.5 x 2^1 = 1.0, 0.5 x 2^2 = 2.0, 0.5 x 2^3 = 4.0 ... 0.5 x 2^n,
 906   // In all the above cases, normalized mantissa returned by frexp routine will
 907   // be exactly equal to 0.5 while exponent will be 0,1,2,3...n
 908   // Perform division to multiplication transform only if divisor is a POT value.
 909   if(frexp((double)f, &exp) != 0.5) { return nullptr; }
 910 
 911   // Limit the range of acceptable exponents
 912   if(exp < -14 || exp > 15) { return nullptr; }
 913 
 914   // Since divisor is a POT number, hence its reciprocal will never
 915   // overflow 11 bits precision range of Float16
 916   // value if exponent returned by frexp routine strictly lie
 917   // within the exponent range of normal min(0x1.0P-14) and
 918   // normal max(0x1.ffcP+15) values.
 919   // Thus we can safely compute the reciprocal of divisor without
 920   // any concerns about the precision loss and transform the division
 921   // into a multiplication operation.
 922   float reciprocal = ((float)1.0) / f;
 923 
 924   assert(frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2");
 925 
 926   // return multiplication by the reciprocal
 927   return (new MulHFNode(in(1), phase->makecon(TypeH::make(reciprocal))));
 928 }
 929 
 930 //=============================================================================
 931 //------------------------------Value------------------------------------------
 932 // An DivDNode divides its inputs.  The third input is a Control input, used to
 933 // prevent hoisting the divide above an unsafe test.
 934 const Type* DivDNode::Value(PhaseGVN* phase) const {
 935   // Either input is TOP ==> the result is TOP
 936   const Type *t1 = phase->type( in(1) );
 937   const Type *t2 = phase->type( in(2) );
 938   if( t1 == Type::TOP ) return Type::TOP;
 939   if( t2 == Type::TOP ) return Type::TOP;
 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   // x/x == 1, we ignore 0/0.
 948   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 949   // Does not work for variables because of NaN's
 950   if (in(1) == in(2) && t1->base() == Type::DoubleCon &&
 951       !g_isnan(t1->getd()) && g_isfinite(t1->getd()) && t1->getd() != 0.0) { // could be negative ZERO or NaN
 952     return TypeD::ONE;
 953   }
 954 
 955   if( t2 == TypeD::ONE )
 956     return t1;
 957 
 958   // If divisor is a constant and not zero, divide them numbers
 959   if( t1->base() == Type::DoubleCon &&
 960       t2->base() == Type::DoubleCon &&
 961       t2->getd() != 0.0 ) // could be negative zero
 962     return TypeD::make( t1->getd()/t2->getd() );
 963 
 964   // If the dividend is a constant zero
 965   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 966   // Test TypeF::ZERO is not sufficient as it could be negative zero
 967   if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )
 968     return TypeD::ZERO;
 969 
 970   // Otherwise we give up all hope
 971   return Type::DOUBLE;
 972 }
 973 
 974 
 975 //------------------------------isA_Copy---------------------------------------
 976 // Dividing by self is 1.
 977 // If the divisor is 1, we are an identity on the dividend.
 978 Node* DivDNode::Identity(PhaseGVN* phase) {
 979   return (phase->type( in(2) ) == TypeD::ONE) ? in(1) : this;
 980 }
 981 
 982 //------------------------------Idealize---------------------------------------
 983 Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 984   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 985   // Don't bother trying to transform a dead node
 986   if( in(0) && in(0)->is_top() )  return nullptr;
 987 
 988   const Type *t2 = phase->type( in(2) );
 989   if( t2 == TypeD::ONE )         // Identity?
 990     return nullptr;              // Skip it
 991 
 992   const TypeD *td = t2->isa_double_constant();
 993   if( !td ) return nullptr;
 994   if( td->base() != Type::DoubleCon ) return nullptr;
 995 
 996   // Check for out of range values
 997   if( td->is_nan() || !td->is_finite() ) return nullptr;
 998 
 999   // Get the value
1000   double d = td->getd();
1001   int exp;
1002 
1003   // Only for special case of dividing by a power of 2
1004   if( frexp(d, &exp) != 0.5 ) return nullptr;
1005 
1006   // Limit the range of acceptable exponents
1007   if( exp < -1021 || exp > 1022 ) return nullptr;
1008 
1009   // Compute the reciprocal
1010   double reciprocal = 1.0 / d;
1011 
1012   assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
1013 
1014   // return multiplication by the reciprocal
1015   return (new MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
1016 }
1017 
1018 //=============================================================================
1019 //------------------------------Identity---------------------------------------
1020 // If the divisor is 1, we are an identity on the dividend.
1021 Node* UDivINode::Identity(PhaseGVN* phase) {
1022   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
1023 }
1024 //------------------------------Value------------------------------------------
1025 // A UDivINode divides its inputs.  The third input is a Control input, used to
1026 // prevent hoisting the divide above an unsafe test.
1027 const Type* UDivINode::Value(PhaseGVN* phase) const {
1028   // Either input is TOP ==> the result is TOP
1029   const Type *t1 = phase->type( in(1) );
1030   const Type *t2 = phase->type( in(2) );
1031   if( t1 == Type::TOP ) return Type::TOP;
1032   if( t2 == Type::TOP ) return Type::TOP;
1033 
1034   // x/x == 1 since we always generate the dynamic divisor check for 0.
1035   if (in(1) == in(2)) {
1036     return TypeInt::ONE;
1037   }
1038 
1039   // Either input is BOTTOM ==> the result is the local BOTTOM
1040   const Type *bot = bottom_type();
1041   if( (t1 == bot) || (t2 == bot) ||
1042       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1043     return bot;
1044 
1045   // Otherwise we give up all hope
1046   return TypeInt::INT;
1047 }
1048 
1049 //------------------------------Idealize---------------------------------------
1050 Node *UDivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
1051   return unsigned_div_ideal<TypeInt, juint>(phase, can_reshape, this);
1052 }
1053 
1054 //=============================================================================
1055 //------------------------------Identity---------------------------------------
1056 // If the divisor is 1, we are an identity on the dividend.
1057 Node* UDivLNode::Identity(PhaseGVN* phase) {
1058   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
1059 }
1060 //------------------------------Value------------------------------------------
1061 // A UDivLNode divides its inputs.  The third input is a Control input, used to
1062 // prevent hoisting the divide above an unsafe test.
1063 const Type* UDivLNode::Value(PhaseGVN* phase) const {
1064   // Either input is TOP ==> the result is TOP
1065   const Type *t1 = phase->type( in(1) );
1066   const Type *t2 = phase->type( in(2) );
1067   if( t1 == Type::TOP ) return Type::TOP;
1068   if( t2 == Type::TOP ) return Type::TOP;
1069 
1070   // x/x == 1 since we always generate the dynamic divisor check for 0.
1071   if (in(1) == in(2)) {
1072     return TypeLong::ONE;
1073   }
1074 
1075   // Either input is BOTTOM ==> the result is the local BOTTOM
1076   const Type *bot = bottom_type();
1077   if( (t1 == bot) || (t2 == bot) ||
1078       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1079     return bot;
1080 
1081   // Otherwise we give up all hope
1082   return TypeLong::LONG;
1083 }
1084 
1085 //------------------------------Idealize---------------------------------------
1086 Node *UDivLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1087   return unsigned_div_ideal<TypeLong, julong>(phase, can_reshape, this);
1088 }
1089 
1090 //=============================================================================
1091 //------------------------------Idealize---------------------------------------
1092 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
1093   // Check for dead control input
1094   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
1095   // Don't bother trying to transform a dead node
1096   if( in(0) && in(0)->is_top() )  return nullptr;
1097 
1098   // Get the modulus
1099   const Type *t = phase->type( in(2) );
1100   if( t == Type::TOP ) return nullptr;
1101   const TypeInt *ti = t->is_int();
1102 
1103   // Check for useless control input
1104   // Check for excluding mod-zero case
1105   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
1106     set_req(0, nullptr);        // Yank control input
1107     return this;
1108   }
1109 
1110   // See if we are MOD'ing by 2^k or 2^k-1.
1111   if( !ti->is_con() ) return nullptr;
1112   jint con = ti->get_con();
1113 
1114   // First, special check for modulo 2^k-1
1115   if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
1116     uint k = exact_log2(con+1);  // Extract k
1117 
1118     // Basic algorithm by David Detlefs.  See fastmod_int.java for gory details.
1119     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*/};
1120     int trip_count = 1;
1121     if( k < ARRAY_SIZE(unroll_factor))  trip_count = unroll_factor[k];
1122 
1123     // If the unroll factor is not too large, and if conditional moves are
1124     // ok, then use this case
1125     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1126       Node *x = in(1);            // Value being mod'd
1127       Node *divisor = in(2);      // Also is mask
1128 
1129       // Add a use to x to prevent it from dying
1130       Node* hook = new Node(1);
1131       hook->init_req(0, x);
1132       // Generate code to reduce X rapidly to nearly 2^k-1.
1133       for( int i = 0; i < trip_count; i++ ) {
1134         Node *xl = phase->transform( new AndINode(x,divisor) );
1135         Node *xh = phase->transform( new RShiftINode(x,phase->intcon(k)) ); // Must be signed
1136         x = phase->transform( new AddINode(xh,xl) );
1137         hook->set_req(0, x);
1138       }
1139 
1140       // Generate sign-fixup code.  Was original value positive?
1141       // int hack_res = (i >= 0) ? divisor : 1;
1142       Node *cmp1 = phase->transform( new CmpINode( in(1), phase->intcon(0) ) );
1143       Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
1144       Node *cmov1= phase->transform( new CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
1145       // if( x >= hack_res ) x -= divisor;
1146       Node *sub  = phase->transform( new SubINode( x, divisor ) );
1147       Node *cmp2 = phase->transform( new CmpINode( x, cmov1 ) );
1148       Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
1149       // Convention is to not transform the return value of an Ideal
1150       // since Ideal is expected to return a modified 'this' or a new node.
1151       Node *cmov2= new CMoveINode(bol2, x, sub, TypeInt::INT);
1152       // cmov2 is now the mod
1153 
1154       // Now remove the bogus extra edges used to keep things alive
1155       hook->destruct(phase);
1156       return cmov2;
1157     }
1158   }
1159 
1160   // Fell thru, the unroll case is not appropriate. Transform the modulo
1161   // into a long multiply/int multiply/subtract case
1162 
1163   // Cannot handle mod 0, and min_jint isn't handled by the transform
1164   if( con == 0 || con == min_jint ) return nullptr;
1165 
1166   // Get the absolute value of the constant; at this point, we can use this
1167   jint pos_con = (con >= 0) ? con : -con;
1168 
1169   // integer Mod 1 is always 0
1170   if( pos_con == 1 ) return new ConINode(TypeInt::ZERO);
1171 
1172   int log2_con = -1;
1173 
1174   // If this is a power of two, they maybe we can mask it
1175   if (is_power_of_2(pos_con)) {
1176     log2_con = log2i_exact(pos_con);
1177 
1178     const Type *dt = phase->type(in(1));
1179     const TypeInt *dti = dt->isa_int();
1180 
1181     // See if this can be masked, if the dividend is non-negative
1182     if( dti && dti->_lo >= 0 )
1183       return ( new AndINode( in(1), phase->intcon( pos_con-1 ) ) );
1184   }
1185 
1186   // Save in(1) so that it cannot be changed or deleted
1187   Node* hook = new Node(1);
1188   hook->init_req(0, in(1));
1189 
1190   // Divide using the transform from DivI to MulL
1191   Node *result = transform_int_divide( phase, in(1), pos_con );
1192   if (result != nullptr) {
1193     Node *divide = phase->transform(result);
1194 
1195     // Re-multiply, using a shift if this is a power of two
1196     Node *mult = nullptr;
1197 
1198     if( log2_con >= 0 )
1199       mult = phase->transform( new LShiftINode( divide, phase->intcon( log2_con ) ) );
1200     else
1201       mult = phase->transform( new MulINode( divide, phase->intcon( pos_con ) ) );
1202 
1203     // Finally, subtract the multiplied divided value from the original
1204     result = new SubINode( in(1), mult );
1205   }
1206 
1207   // Now remove the bogus extra edges used to keep things alive
1208   hook->destruct(phase);
1209 
1210   // return the value
1211   return result;
1212 }
1213 
1214 //------------------------------Value------------------------------------------
1215 static const Type* mod_value(const PhaseGVN* phase, const Node* in1, const Node* in2, const BasicType bt) {
1216   assert(bt == T_INT || bt == T_LONG, "unexpected basic type");
1217   // Either input is TOP ==> the result is TOP
1218   const Type* t1 = phase->type(in1);
1219   const Type* t2 = phase->type(in2);
1220   if (t1 == Type::TOP) { return Type::TOP; }
1221   if (t2 == Type::TOP) { return Type::TOP; }
1222 
1223   // Mod by zero?  Throw exception at runtime!
1224   if (t2 == TypeInteger::zero(bt)) {
1225     return Type::TOP;
1226   }
1227 
1228   // We always generate the dynamic check for 0.
1229   // 0 MOD X is 0
1230   if (t1 == TypeInteger::zero(bt)) { return t1; }
1231 
1232   // X MOD X is 0
1233   if (in1 == in2) {
1234     return TypeInteger::zero(bt);
1235   }
1236 
1237   const TypeInteger* i1 = t1->is_integer(bt);
1238   const TypeInteger* i2 = t2->is_integer(bt);
1239   if (i1->is_con() && i2->is_con()) {
1240     // We must be modulo'ing 2 int constants.
1241     // Special case: min_jlong % '-1' is UB, and e.g., x86 triggers a division error.
1242     // Any value % -1 is 0, so we can return 0 and avoid that scenario.
1243     if (i2->get_con_as_long(bt) == -1) {
1244       return TypeInteger::zero(bt);
1245     }
1246     return TypeInteger::make(i1->get_con_as_long(bt) % i2->get_con_as_long(bt), bt);
1247   }
1248   // We checked that t2 is not the zero constant. Hence, at least i2->_lo or i2->_hi must be non-zero,
1249   // and hence its absoute value is bigger than zero. Hence, the magnitude of the divisor (i.e. the
1250   // largest absolute value for any value in i2) must be in the range [1, 2^31] or [1, 2^63], depending
1251   // on the BasicType.
1252   julong divisor_magnitude = MAX2(g_uabs(i2->lo_as_long()), g_uabs(i2->hi_as_long()));
1253   // JVMS lrem bytecode: "the magnitude of the result is always less than the magnitude of the divisor"
1254   // "less than" means we can subtract 1 to get an inclusive upper bound in [0, 2^31-1] or [0, 2^63-1], respectively
1255   jlong hi = static_cast<jlong>(divisor_magnitude - 1);
1256   jlong lo = -hi;
1257   // JVMS lrem bytecode: "the result of the remainder operation can be negative only if the dividend
1258   // is negative and can be positive only if the dividend is positive"
1259   // Note that with a dividend with bounds e.g. lo == -4 and hi == -1 can still result in values
1260   // below lo; i.e., -3 % 3 == 0.
1261   // That means we cannot restrict the bound that is closer to zero beyond knowing its sign (or zero).
1262   if (i1->hi_as_long() <= 0) {
1263     // all dividends are not positive, so the result is not positive
1264     hi = 0;
1265     // if the dividend is known to be closer to zero, use that as a lower limit
1266     lo = MAX2(lo, i1->lo_as_long());
1267   } else if (i1->lo_as_long() >= 0) {
1268     // all dividends are not negative, so the result is not negative
1269     lo = 0;
1270     // if the dividend is known to be closer to zero, use that as an upper limit
1271     hi = MIN2(hi, i1->hi_as_long());
1272   } else {
1273     // Mixed signs, so we don't know the sign of the result, but the result is
1274     // either the dividend itself or a value closer to zero than the dividend,
1275     // and it is closer to zero than the divisor.
1276     // As we know i1->_lo < 0 and i1->_hi > 0, we can use these bounds directly.
1277     lo = MAX2(lo, i1->lo_as_long());
1278     hi = MIN2(hi, i1->hi_as_long());
1279   }
1280   return TypeInteger::make(lo, hi, MAX2(i1->_widen, i2->_widen), bt);
1281 }
1282 
1283 const Type* ModINode::Value(PhaseGVN* phase) const {
1284   return mod_value(phase, in(1), in(2), T_INT);
1285 }
1286 
1287 //=============================================================================
1288 //------------------------------Idealize---------------------------------------
1289 
1290 template <typename TypeClass, typename Unsigned>
1291 static Node* unsigned_mod_ideal(PhaseGVN* phase, bool can_reshape, Node* mod) {
1292   // Check for dead control input
1293   if (mod->in(0) != nullptr && mod->remove_dead_region(phase, can_reshape)) {
1294     return mod;
1295   }
1296   // Don't bother trying to transform a dead node
1297   if (mod->in(0) != nullptr && mod->in(0)->is_top()) {
1298     return nullptr;
1299   }
1300 
1301   // Get the modulus
1302   const Type* t = phase->type(mod->in(2));
1303   if (t == Type::TOP) {
1304     return nullptr;
1305   }
1306   const TypeClass* type_divisor = t->cast<TypeClass>();
1307 
1308   // Check for useless control input
1309   // Check for excluding mod-zero case
1310   if (mod->in(0) != nullptr && (type_divisor->_hi < 0 || type_divisor->_lo > 0)) {
1311     mod->set_req(0, nullptr); // Yank control input
1312     return mod;
1313   }
1314 
1315   if (!type_divisor->is_con()) {
1316     return nullptr;
1317   }
1318   Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con());
1319 
1320   if (divisor == 0) {
1321     return nullptr;
1322   }
1323 
1324   if (is_power_of_2(divisor)) {
1325     return make_and<TypeClass>(mod->in(1), phase->makecon(TypeClass::make(divisor - 1)));
1326   }
1327 
1328   return nullptr;
1329 }
1330 
1331 template <typename TypeClass, typename Unsigned, typename Signed>
1332 static const Type* unsigned_mod_value(PhaseGVN* phase, const Node* mod) {
1333   const Type* t1 = phase->type(mod->in(1));
1334   const Type* t2 = phase->type(mod->in(2));
1335   if (t1 == Type::TOP) {
1336     return Type::TOP;
1337   }
1338   if (t2 == Type::TOP) {
1339     return Type::TOP;
1340   }
1341 
1342   // 0 MOD X is 0
1343   if (t1 == TypeClass::ZERO) {
1344     return TypeClass::ZERO;
1345   }
1346   // X MOD X is 0
1347   if (mod->in(1) == mod->in(2)) {
1348     return TypeClass::ZERO;
1349   }
1350 
1351   // Either input is BOTTOM ==> the result is the local BOTTOM
1352   const Type* bot = mod->bottom_type();
1353   if ((t1 == bot) || (t2 == bot) ||
1354       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM)) {
1355     return bot;
1356   }
1357 
1358   const TypeClass* type_divisor = t2->cast<TypeClass>();
1359   if (type_divisor->is_con() && type_divisor->get_con() == 1) {
1360     return TypeClass::ZERO;
1361   }
1362 
1363   // Mod by zero?  Throw an exception at runtime!
1364   if (type_divisor->is_con() && type_divisor->get_con() == 0) {
1365     return TypeClass::POS;
1366   }
1367 
1368   const TypeClass* type_dividend = t1->cast<TypeClass>();
1369   if (type_dividend->is_con() && type_divisor->is_con()) {
1370     Unsigned dividend = static_cast<Unsigned>(type_dividend->get_con());
1371     Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con());
1372     return TypeClass::make(static_cast<Signed>(dividend % divisor));
1373   }
1374 
1375   return bot;
1376 }
1377 
1378 Node* UModINode::Ideal(PhaseGVN* phase, bool can_reshape) {
1379   return unsigned_mod_ideal<TypeInt, juint>(phase, can_reshape, this);
1380 }
1381 
1382 const Type* UModINode::Value(PhaseGVN* phase) const {
1383   return unsigned_mod_value<TypeInt, juint, jint>(phase, this);
1384 }
1385 
1386 //=============================================================================
1387 //------------------------------Idealize---------------------------------------
1388 Node *ModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1389   // Check for dead control input
1390   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
1391   // Don't bother trying to transform a dead node
1392   if( in(0) && in(0)->is_top() )  return nullptr;
1393 
1394   // Get the modulus
1395   const Type *t = phase->type( in(2) );
1396   if( t == Type::TOP ) return nullptr;
1397   const TypeLong *tl = t->is_long();
1398 
1399   // Check for useless control input
1400   // Check for excluding mod-zero case
1401   if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
1402     set_req(0, nullptr);        // Yank control input
1403     return this;
1404   }
1405 
1406   // See if we are MOD'ing by 2^k or 2^k-1.
1407   if( !tl->is_con() ) return nullptr;
1408   jlong con = tl->get_con();
1409 
1410   // Expand mod
1411   if(con >= 0 && con < max_jlong && is_power_of_2(con + 1)) {
1412     uint k = log2i_exact(con + 1);  // Extract k
1413 
1414     // Basic algorithm by David Detlefs.  See fastmod_long.java for gory details.
1415     // Used to help a popular random number generator which does a long-mod
1416     // of 2^31-1 and shows up in SpecJBB and SciMark.
1417     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*/};
1418     int trip_count = 1;
1419     if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
1420 
1421     // If the unroll factor is not too large, and if conditional moves are
1422     // ok, then use this case
1423     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1424       Node *x = in(1);            // Value being mod'd
1425       Node *divisor = in(2);      // Also is mask
1426 
1427       // Add a use to x to prevent it from dying
1428       Node* hook = new Node(1);
1429       hook->init_req(0, x);
1430       // Generate code to reduce X rapidly to nearly 2^k-1.
1431       for( int i = 0; i < trip_count; i++ ) {
1432         Node *xl = phase->transform( new AndLNode(x,divisor) );
1433         Node *xh = phase->transform( new RShiftLNode(x,phase->intcon(k)) ); // Must be signed
1434         x = phase->transform( new AddLNode(xh,xl) );
1435         hook->set_req(0, x);    // Add a use to x to prevent it from dying
1436       }
1437 
1438       // Generate sign-fixup code.  Was original value positive?
1439       // long hack_res = (i >= 0) ? divisor : CONST64(1);
1440       Node *cmp1 = phase->transform( new CmpLNode( in(1), phase->longcon(0) ) );
1441       Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
1442       Node *cmov1= phase->transform( new CMoveLNode(bol1, phase->longcon(1), divisor, TypeLong::LONG) );
1443       // if( x >= hack_res ) x -= divisor;
1444       Node *sub  = phase->transform( new SubLNode( x, divisor ) );
1445       Node *cmp2 = phase->transform( new CmpLNode( x, cmov1 ) );
1446       Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
1447       // Convention is to not transform the return value of an Ideal
1448       // since Ideal is expected to return a modified 'this' or a new node.
1449       Node *cmov2= new CMoveLNode(bol2, x, sub, TypeLong::LONG);
1450       // cmov2 is now the mod
1451 
1452       // Now remove the bogus extra edges used to keep things alive
1453       hook->destruct(phase);
1454       return cmov2;
1455     }
1456   }
1457 
1458   // Fell thru, the unroll case is not appropriate. Transform the modulo
1459   // into a long multiply/int multiply/subtract case
1460 
1461   // Cannot handle mod 0, and min_jlong isn't handled by the transform
1462   if( con == 0 || con == min_jlong ) return nullptr;
1463 
1464   // Get the absolute value of the constant; at this point, we can use this
1465   jlong pos_con = (con >= 0) ? con : -con;
1466 
1467   // integer Mod 1 is always 0
1468   if( pos_con == 1 ) return new ConLNode(TypeLong::ZERO);
1469 
1470   int log2_con = -1;
1471 
1472   // If this is a power of two, then maybe we can mask it
1473   if (is_power_of_2(pos_con)) {
1474     log2_con = log2i_exact(pos_con);
1475 
1476     const Type *dt = phase->type(in(1));
1477     const TypeLong *dtl = dt->isa_long();
1478 
1479     // See if this can be masked, if the dividend is non-negative
1480     if( dtl && dtl->_lo >= 0 )
1481       return ( new AndLNode( in(1), phase->longcon( pos_con-1 ) ) );
1482   }
1483 
1484   // Save in(1) so that it cannot be changed or deleted
1485   // Add a use to x to prevent him from dying
1486   Node* hook = new Node(1);
1487   hook->init_req(0, in(1));
1488 
1489   // Divide using the transform from DivL to MulL
1490   Node *result = transform_long_divide( phase, in(1), pos_con );
1491   if (result != nullptr) {
1492     Node *divide = phase->transform(result);
1493 
1494     // Re-multiply, using a shift if this is a power of two
1495     Node *mult = nullptr;
1496 
1497     if( log2_con >= 0 )
1498       mult = phase->transform( new LShiftLNode( divide, phase->intcon( log2_con ) ) );
1499     else
1500       mult = phase->transform( new MulLNode( divide, phase->longcon( pos_con ) ) );
1501 
1502     // Finally, subtract the multiplied divided value from the original
1503     result = new SubLNode( in(1), mult );
1504   }
1505 
1506   // Now remove the bogus extra edges used to keep things alive
1507   hook->destruct(phase);
1508 
1509   // return the value
1510   return result;
1511 }
1512 
1513 //------------------------------Value------------------------------------------
1514 const Type* ModLNode::Value(PhaseGVN* phase) const {
1515   return mod_value(phase, in(1), in(2), T_LONG);
1516 }
1517 
1518 Node *UModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1519   return unsigned_mod_ideal<TypeLong, julong>(phase, can_reshape, this);
1520 }
1521 
1522 const Type* UModLNode::Value(PhaseGVN* phase) const {
1523   return unsigned_mod_value<TypeLong, julong, jlong>(phase, this);
1524 }
1525 
1526 const Type* ModFNode::get_result_if_constant(const Type* dividend, const Type* divisor) const {
1527   // If either number is not a constant, we know nothing.
1528   if ((dividend->base() != Type::FloatCon) || (divisor->base() != Type::FloatCon)) {
1529     return nullptr; // note: x%x can be either NaN or 0
1530   }
1531 
1532   float dividend_f = dividend->getf();
1533   float divisor_f = divisor->getf();
1534   jint dividend_i = jint_cast(dividend_f); // note:  *(int*)&f1, not just (int)f1
1535   jint divisor_i = jint_cast(divisor_f);
1536 
1537   // If either is a NaN, return an input NaN
1538   if (g_isnan(dividend_f)) {
1539     return dividend;
1540   }
1541   if (g_isnan(divisor_f)) {
1542     return divisor;
1543   }
1544 
1545   // If an operand is infinity or the divisor is +/- zero, punt.
1546   if (!g_isfinite(dividend_f) || !g_isfinite(divisor_f) || divisor_i == 0 || divisor_i == min_jint) {
1547     return nullptr;
1548   }
1549 
1550   // We must be modulo'ing 2 float constants.
1551   // Make sure that the sign of the fmod is equal to the sign of the dividend
1552   jint xr = jint_cast(fmod(dividend_f, divisor_f));
1553   if ((dividend_i ^ xr) < 0) {
1554     xr ^= min_jint;
1555   }
1556 
1557   return TypeF::make(jfloat_cast(xr));
1558 }
1559 
1560 const Type* ModDNode::get_result_if_constant(const Type* dividend, const Type* divisor) const {
1561   // If either number is not a constant, we know nothing.
1562   if ((dividend->base() != Type::DoubleCon) || (divisor->base() != Type::DoubleCon)) {
1563     return nullptr; // note: x%x can be either NaN or 0
1564   }
1565 
1566   double dividend_d = dividend->getd();
1567   double divisor_d = divisor->getd();
1568   jlong dividend_l = jlong_cast(dividend_d); // note:  *(long*)&f1, not just (long)f1
1569   jlong divisor_l = jlong_cast(divisor_d);
1570 
1571   // If either is a NaN, return an input NaN
1572   if (g_isnan(dividend_d)) {
1573     return dividend;
1574   }
1575   if (g_isnan(divisor_d)) {
1576     return divisor;
1577   }
1578 
1579   // If an operand is infinity or the divisor is +/- zero, punt.
1580   if (!g_isfinite(dividend_d) || !g_isfinite(divisor_d) || divisor_l == 0 || divisor_l == min_jlong) {
1581     return nullptr;
1582   }
1583 
1584   // We must be modulo'ing 2 double constants.
1585   // Make sure that the sign of the fmod is equal to the sign of the dividend
1586   jlong xr = jlong_cast(fmod(dividend_d, divisor_d));
1587   if ((dividend_l ^ xr) < 0) {
1588     xr ^= min_jlong;
1589   }
1590 
1591   return TypeD::make(jdouble_cast(xr));
1592 }
1593 
1594 const Type* ModFloatingNode::Value(PhaseGVN* phase) const {
1595   const Type* t = CallLeafPureNode::Value(phase);
1596   if (t == Type::TOP) { return Type::TOP; }
1597   const Type* dividend_type = phase->type(dividend());
1598   const Type* divisor_type = phase->type(divisor());
1599   if (dividend_type == Type::TOP || divisor_type == Type::TOP) {
1600     return Type::TOP;
1601   }
1602   const Type* constant_result = get_result_if_constant(dividend_type, divisor_type);
1603   if (constant_result != nullptr) {
1604     const TypeTuple* tt = t->is_tuple();
1605     uint cnt = tt->cnt();
1606     uint param_cnt = cnt - TypeFunc::Parms;
1607     const Type** fields = TypeTuple::fields(param_cnt);
1608     fields[TypeFunc::Parms] = constant_result;
1609     if (param_cnt > 1) { fields[TypeFunc::Parms + 1] = Type::HALF; }
1610     return TypeTuple::make(cnt, fields);
1611   }
1612   return t;
1613 }
1614 
1615 //=============================================================================
1616 
1617 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
1618   init_req(0, c);
1619   init_req(1, dividend);
1620   init_req(2, divisor);
1621 }
1622 
1623 DivModNode* DivModNode::make(Node* div_or_mod, BasicType bt, bool is_unsigned) {
1624   assert(bt == T_INT || bt == T_LONG, "only int or long input pattern accepted");
1625 
1626   if (bt == T_INT) {
1627     if (is_unsigned) {
1628       return UDivModINode::make(div_or_mod);
1629     } else {
1630       return DivModINode::make(div_or_mod);
1631     }
1632   } else {
1633     if (is_unsigned) {
1634       return UDivModLNode::make(div_or_mod);
1635     } else {
1636       return DivModLNode::make(div_or_mod);
1637     }
1638   }
1639 }
1640 
1641 //------------------------------make------------------------------------------
1642 DivModINode* DivModINode::make(Node* div_or_mod) {
1643   Node* n = div_or_mod;
1644   assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
1645          "only div or mod input pattern accepted");
1646 
1647   DivModINode* divmod = new DivModINode(n->in(0), n->in(1), n->in(2));
1648   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1649   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1650   return divmod;
1651 }
1652 
1653 //------------------------------make------------------------------------------
1654 DivModLNode* DivModLNode::make(Node* div_or_mod) {
1655   Node* n = div_or_mod;
1656   assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
1657          "only div or mod input pattern accepted");
1658 
1659   DivModLNode* divmod = new DivModLNode(n->in(0), n->in(1), n->in(2));
1660   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1661   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1662   return divmod;
1663 }
1664 
1665 //------------------------------match------------------------------------------
1666 // return result(s) along with their RegMask info
1667 Node *DivModINode::match( const ProjNode *proj, const Matcher *match ) {
1668   uint ideal_reg = proj->ideal_reg();
1669   RegMask rm;
1670   if (proj->_con == div_proj_num) {
1671     rm.assignFrom(match->divI_proj_mask());
1672   } else {
1673     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1674     rm.assignFrom(match->modI_proj_mask());
1675   }
1676   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1677 }
1678 
1679 
1680 //------------------------------match------------------------------------------
1681 // return result(s) along with their RegMask info
1682 Node *DivModLNode::match( const ProjNode *proj, const Matcher *match ) {
1683   uint ideal_reg = proj->ideal_reg();
1684   RegMask rm;
1685   if (proj->_con == div_proj_num) {
1686     rm.assignFrom(match->divL_proj_mask());
1687   } else {
1688     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1689     rm.assignFrom(match->modL_proj_mask());
1690   }
1691   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1692 }
1693 
1694 //------------------------------make------------------------------------------
1695 UDivModINode* UDivModINode::make(Node* div_or_mod) {
1696   Node* n = div_or_mod;
1697   assert(n->Opcode() == Op_UDivI || n->Opcode() == Op_UModI,
1698          "only div or mod input pattern accepted");
1699 
1700   UDivModINode* divmod = new UDivModINode(n->in(0), n->in(1), n->in(2));
1701   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1702   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1703   return divmod;
1704 }
1705 
1706 //------------------------------make------------------------------------------
1707 UDivModLNode* UDivModLNode::make(Node* div_or_mod) {
1708   Node* n = div_or_mod;
1709   assert(n->Opcode() == Op_UDivL || n->Opcode() == Op_UModL,
1710          "only div or mod input pattern accepted");
1711 
1712   UDivModLNode* divmod = new UDivModLNode(n->in(0), n->in(1), n->in(2));
1713   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1714   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1715   return divmod;
1716 }
1717 
1718 //------------------------------match------------------------------------------
1719 // return result(s) along with their RegMask info
1720 Node* UDivModINode::match( const ProjNode *proj, const Matcher *match ) {
1721   uint ideal_reg = proj->ideal_reg();
1722   RegMask rm;
1723   if (proj->_con == div_proj_num) {
1724     rm.assignFrom(match->divI_proj_mask());
1725   } else {
1726     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1727     rm.assignFrom(match->modI_proj_mask());
1728   }
1729   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1730 }
1731 
1732 
1733 //------------------------------match------------------------------------------
1734 // return result(s) along with their RegMask info
1735 Node* UDivModLNode::match( const ProjNode *proj, const Matcher *match ) {
1736   uint ideal_reg = proj->ideal_reg();
1737   RegMask rm;
1738   if (proj->_con == div_proj_num) {
1739     rm.assignFrom(match->divL_proj_mask());
1740   } else {
1741     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1742     rm.assignFrom(match->modL_proj_mask());
1743   }
1744   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1745 }