1 /*
   2  * Copyright (c) 1997, 2025, 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).
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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
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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 if ( !Matcher::use_asm_for_ldiv_by_con(d) ) { // Use hardware DIV instruction when
 423                                                        // it is faster than code generated below.
 424     // Attempt the jlong constant divide -> multiply transform found in
 425     //   "Division by Invariant Integers using Multiplication"
 426     //     by Granlund and Montgomery
 427     // See also "Hacker's Delight", chapter 10 by Warren.
 428 
 429     jlong magic_const;
 430     jint shift_const;
 431     if (magic_long_divide_constants(d, magic_const, shift_const)) {
 432       // Compute the high half of the dividend x magic multiplication
 433       Node *mul_hi = phase->transform(long_by_long_mulhi(phase, dividend, magic_const));
 434 
 435       // The high half of the 128-bit multiply is computed.
 436       if (magic_const < 0) {
 437         // The magic multiplier is too large for a 64 bit constant. We've adjusted
 438         // it down by 2^64, but have to add 1 dividend back in after the multiplication.
 439         // This handles the "overflow" case described by Granlund and Montgomery.
 440         mul_hi = phase->transform(new AddLNode(dividend, mul_hi));
 441       }
 442 
 443       // Shift over the (adjusted) mulhi
 444       if (shift_const != 0) {
 445         mul_hi = phase->transform(new RShiftLNode(mul_hi, phase->intcon(shift_const)));
 446       }
 447 
 448       // Get a 0 or -1 from the sign of the dividend.
 449       Node *addend0 = mul_hi;
 450       Node *addend1 = phase->transform(new RShiftLNode(dividend, phase->intcon(N-1)));
 451 
 452       // If the divisor is negative, swap the order of the input addends;
 453       // this has the effect of negating the quotient.
 454       if (!d_pos) {
 455         Node *temp = addend0; addend0 = addend1; addend1 = temp;
 456       }
 457 
 458       // Adjust the final quotient by subtracting -1 (adding 1)
 459       // from the mul_hi.
 460       q = new SubLNode(addend0, addend1);
 461     }
 462   }
 463 
 464   return q;
 465 }
 466 
 467 template <typename TypeClass, typename Unsigned>
 468 Node* unsigned_div_ideal(PhaseGVN* phase, bool can_reshape, Node* div) {
 469   // Check for dead control input
 470   if (div->in(0) != nullptr && div->remove_dead_region(phase, can_reshape)) {
 471     return div;
 472   }
 473   // Don't bother trying to transform a dead node
 474   if (div->in(0) != nullptr && div->in(0)->is_top()) {
 475     return nullptr;
 476   }
 477 
 478   const Type* t = phase->type(div->in(2));
 479   if (t == Type::TOP) {
 480     return nullptr;
 481   }
 482   const TypeClass* type_divisor = t->cast<TypeClass>();
 483 
 484   // Check for useless control input
 485   // Check for excluding div-zero case
 486   if (div->in(0) != nullptr && (type_divisor->_hi < 0 || type_divisor->_lo > 0)) {
 487     div->set_req(0, nullptr); // Yank control input
 488     return div;
 489   }
 490 
 491   if (!type_divisor->is_con()) {
 492     return nullptr;
 493   }
 494   Unsigned divisor = static_cast<Unsigned>(type_divisor->get_con()); // Get divisor
 495 
 496   if (divisor == 0 || divisor == 1) {
 497     return nullptr; // Dividing by zero constant does not idealize
 498   }
 499 
 500   if (is_power_of_2(divisor)) {
 501     return make_urshift<TypeClass>(div->in(1), phase->intcon(log2i_graceful(divisor)));
 502   }
 503 
 504   return nullptr;
 505 }
 506 
 507 template<typename IntegerType>
 508 static const IntegerType* compute_signed_div_type(const IntegerType* i1, const IntegerType* i2) {
 509   typedef typename IntegerType::NativeType NativeType;
 510   assert(!i2->is_con() || i2->get_con() != 0, "Can't handle zero constant divisor");
 511   int widen = MAX2(i1->_widen, i2->_widen);
 512 
 513   // Case A: divisor range spans zero (i2->_lo < 0 < i2->_hi)
 514   // We split into two subproblems to avoid division by 0:
 515   //   - negative part: [i2->_lo, −1]
 516   //   - positive part: [1, i2->_hi]
 517   // Then we union the results by taking the min of all lower‐bounds and
 518   // the max of all upper‐bounds from the two halves.
 519   if (i2->_lo < 0 && i2->_hi > 0) {
 520     // Handle negative part of the divisor range
 521     const IntegerType* neg_part = compute_signed_div_type(i1, IntegerType::make(i2->_lo, -1, widen));
 522     // Handle positive part of the divisor range
 523     const IntegerType* pos_part = compute_signed_div_type(i1, IntegerType::make(1, i2->_hi, widen));
 524     // Merge results
 525     NativeType new_lo = MIN2(neg_part->_lo, pos_part->_lo);
 526     NativeType new_hi = MAX2(neg_part->_hi, pos_part->_hi);
 527     assert(new_hi >= new_lo, "sanity");
 528     return IntegerType::make(new_lo, new_hi, widen);
 529   }
 530 
 531   // Case B: divisor range does NOT span zero.
 532   // Here i2 is entirely negative or entirely positive.
 533   // Then i1/i2 is monotonic in i1 and i2 (when i2 keeps the same sign).
 534   // Therefore the extrema occur at the four “corners”:
 535   //   (i1->_lo, i2->_hi), (i1->_lo, i2->_lo), (i1->_hi, i2->_lo), (i1->_hi, i2->_hi).
 536   // We compute all four and take the min and max.
 537   // A special case handles overflow when dividing the most‐negative value by −1.
 538 
 539   // adjust i2 bounds to not include zero, as zero always throws
 540   NativeType i2_lo = i2->_lo == 0 ? 1 : i2->_lo;
 541   NativeType i2_hi = i2->_hi == 0 ? -1 : i2->_hi;
 542   constexpr NativeType min_val = std::numeric_limits<NativeType>::min();
 543   static_assert(min_val == min_jint || min_val == min_jlong, "min has to be either min_jint or min_jlong");
 544   constexpr NativeType max_val = std::numeric_limits<NativeType>::max();
 545   static_assert(max_val == max_jint || max_val == max_jlong, "max has to be either max_jint or max_jlong");
 546 
 547   // Special overflow case: min_val / (-1) == min_val (cf. JVMS§6.5 idiv/ldiv)
 548   // We need to be careful that we never run min_val / (-1) in C++ code, as this overflow is UB there
 549   if (i1->_lo == min_val && i2_hi == -1) {
 550     NativeType new_lo = min_val;
 551     NativeType new_hi;
 552     // compute new_hi depending on whether divisor or dividend is non-constant.
 553     // i2 is purely in the negative domain here (as i2_hi is -1)
 554     // which means the maximum value this division can yield is either
 555     if (!i1->is_con()) {
 556       // a) non-constant dividend: i1 could be min_val + 1.
 557       // -> i1 / i2 = (min_val + 1) / -1 = max_val is possible.
 558       new_hi = max_val;
 559       assert((min_val + 1) / -1 == new_hi, "new_hi should be max_val");
 560     } else if (i2_lo != i2_hi) {
 561       // b) i1 is constant min_val, i2 is non-constant.
 562       //    if i2 = -1 -> i1 / i2 =  min_val / -1 = min_val
 563       //    if i2 < -1 -> i1 / i2 <= min_val / -2 = (max_val / 2) + 1
 564       new_hi = (max_val / 2) + 1;
 565       assert(min_val / -2 == new_hi, "new_hi should be (max_val / 2) + 1)");
 566     } else {
 567       // c) i1 is constant min_val, i2 is constant -1.
 568       //    -> i1 / i2 = min_val / -1 = min_val
 569       new_hi = min_val;
 570     }
 571 
 572 #ifdef ASSERT
 573     // validate new_hi for non-constant divisor
 574     if (i2_lo != i2_hi) {
 575       assert(i2_lo != -1, "Special case not possible here, as i2_lo has to be < i2_hi");
 576       NativeType result = i1->_lo / i2_lo;
 577       assert(new_hi >= result, "computed wrong value for new_hi");
 578     }
 579 
 580     // validate new_hi for non-constant dividend
 581     if (!i1->is_con()) {
 582       assert(i2_hi > min_val, "Special case not possible here, as i1->_hi has to be > min");
 583       NativeType result1 = i1->_hi / i2_lo;
 584       NativeType result2 = i1->_hi / i2_hi;
 585       assert(new_hi >= result1 && new_hi >= result2, "computed wrong value for new_hi");
 586     }
 587 #endif
 588 
 589     return IntegerType::make(new_lo, new_hi, widen);
 590   }
 591   assert((i1->_lo != min_val && i1->_hi != min_val) || (i2_hi != -1 && i2_lo != -1), "should have filtered out before");
 592 
 593   // Special case not possible here, calculate all corners normally
 594   NativeType corner1 = i1->_lo / i2_lo;
 595   NativeType corner2 = i1->_lo / i2_hi;
 596   NativeType corner3 = i1->_hi / i2_lo;
 597   NativeType corner4 = i1->_hi / i2_hi;
 598 
 599   NativeType new_lo = MIN4(corner1, corner2, corner3, corner4);
 600   NativeType new_hi = MAX4(corner1, corner2, corner3, corner4);
 601   return IntegerType::make(new_lo, new_hi, widen);
 602 }
 603 
 604 //=============================================================================
 605 //------------------------------Identity---------------------------------------
 606 // If the divisor is 1, we are an identity on the dividend.
 607 Node* DivINode::Identity(PhaseGVN* phase) {
 608   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
 609 }
 610 
 611 //------------------------------Idealize---------------------------------------
 612 // Divides can be changed to multiplies and/or shifts
 613 Node *DivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
 614   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 615   // Don't bother trying to transform a dead node
 616   if( in(0) && in(0)->is_top() )  return nullptr;
 617 
 618   const Type *t = phase->type( in(2) );
 619   if( t == TypeInt::ONE )      // Identity?
 620     return nullptr;            // Skip it
 621 
 622   const TypeInt *ti = t->isa_int();
 623   if( !ti ) return nullptr;
 624 
 625   // Check for useless control input
 626   // Check for excluding div-zero case
 627   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
 628     set_req(0, nullptr);           // Yank control input
 629     return this;
 630   }
 631 
 632   if( !ti->is_con() ) return nullptr;
 633   jint i = ti->get_con();       // Get divisor
 634 
 635   if (i == 0) return nullptr;   // Dividing by zero constant does not idealize
 636 
 637   // Dividing by MININT does not optimize as a power-of-2 shift.
 638   if( i == min_jint ) return nullptr;
 639 
 640   return transform_int_divide( phase, in(1), i );
 641 }
 642 
 643 //------------------------------Value------------------------------------------
 644 // A DivINode divides its inputs.  The third input is a Control input, used to
 645 // prevent hoisting the divide above an unsafe test.
 646 const Type* DivINode::Value(PhaseGVN* phase) const {
 647   // Either input is TOP ==> the result is TOP
 648   const Type* t1 = phase->type(in(1));
 649   const Type* t2 = phase->type(in(2));
 650   if (t1 == Type::TOP || t2 == Type::TOP) {
 651     return Type::TOP;
 652   }
 653 
 654   if (t2 == TypeInt::ZERO) {
 655     // this division will always throw an exception
 656     return Type::TOP;
 657   }
 658 
 659   // x/x == 1 since we always generate the dynamic divisor check for 0.
 660   if (in(1) == in(2)) {
 661     return TypeInt::ONE;
 662   }
 663 
 664   const TypeInt* i1 = t1->is_int();
 665   const TypeInt* i2 = t2->is_int();
 666 
 667   return compute_signed_div_type<TypeInt>(i1, i2);
 668 }
 669 
 670 
 671 //=============================================================================
 672 //------------------------------Identity---------------------------------------
 673 // If the divisor is 1, we are an identity on the dividend.
 674 Node* DivLNode::Identity(PhaseGVN* phase) {
 675   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
 676 }
 677 
 678 //------------------------------Idealize---------------------------------------
 679 // Dividing by a power of 2 is a shift.
 680 Node *DivLNode::Ideal( PhaseGVN *phase, bool can_reshape) {
 681   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 682   // Don't bother trying to transform a dead node
 683   if( in(0) && in(0)->is_top() )  return nullptr;
 684 
 685   const Type *t = phase->type( in(2) );
 686   if( t == TypeLong::ONE )      // Identity?
 687     return nullptr;             // Skip it
 688 
 689   const TypeLong *tl = t->isa_long();
 690   if( !tl ) return nullptr;
 691 
 692   // Check for useless control input
 693   // Check for excluding div-zero case
 694   if (in(0) && (tl->_hi < 0 || tl->_lo > 0)) {
 695     set_req(0, nullptr);         // Yank control input
 696     return this;
 697   }
 698 
 699   if( !tl->is_con() ) return nullptr;
 700   jlong l = tl->get_con();      // Get divisor
 701 
 702   if (l == 0) return nullptr;   // Dividing by zero constant does not idealize
 703 
 704   // Dividing by MINLONG does not optimize as a power-of-2 shift.
 705   if( l == min_jlong ) return nullptr;
 706 
 707   return transform_long_divide( phase, in(1), l );
 708 }
 709 
 710 //------------------------------Value------------------------------------------
 711 // A DivLNode divides its inputs.  The third input is a Control input, used to
 712 // prevent hoisting the divide above an unsafe test.
 713 const Type* DivLNode::Value(PhaseGVN* phase) const {
 714   // Either input is TOP ==> the result is TOP
 715   const Type* t1 = phase->type(in(1));
 716   const Type* t2 = phase->type(in(2));
 717   if (t1 == Type::TOP || t2 == Type::TOP) {
 718     return Type::TOP;
 719   }
 720 
 721   if (t2 == TypeLong::ZERO) {
 722     // this division will always throw an exception
 723     return Type::TOP;
 724   }
 725 
 726   // x/x == 1 since we always generate the dynamic divisor check for 0.
 727   if (in(1) == in(2)) {
 728     return TypeLong::ONE;
 729   }
 730 
 731   const TypeLong* i1 = t1->is_long();
 732   const TypeLong* i2 = t2->is_long();
 733 
 734   return compute_signed_div_type<TypeLong>(i1, i2);
 735 }
 736 
 737 
 738 //=============================================================================
 739 //------------------------------Value------------------------------------------
 740 // An DivFNode divides its inputs.  The third input is a Control input, used to
 741 // prevent hoisting the divide above an unsafe test.
 742 const Type* DivFNode::Value(PhaseGVN* phase) const {
 743   // Either input is TOP ==> the result is TOP
 744   const Type *t1 = phase->type( in(1) );
 745   const Type *t2 = phase->type( in(2) );
 746   if( t1 == Type::TOP ) return Type::TOP;
 747   if( t2 == Type::TOP ) return Type::TOP;
 748 
 749   // Either input is BOTTOM ==> the result is the local BOTTOM
 750   const Type *bot = bottom_type();
 751   if( (t1 == bot) || (t2 == bot) ||
 752       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 753     return bot;
 754 
 755   // x/x == 1, we ignore 0/0.
 756   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 757   // Does not work for variables because of NaN's
 758   if (in(1) == in(2) && t1->base() == Type::FloatCon &&
 759       !g_isnan(t1->getf()) && g_isfinite(t1->getf()) && t1->getf() != 0.0) { // could be negative ZERO or NaN
 760     return TypeF::ONE;
 761   }
 762 
 763   if( t2 == TypeF::ONE )
 764     return t1;
 765 
 766   // If divisor is a constant and not zero, divide them numbers
 767   if( t1->base() == Type::FloatCon &&
 768       t2->base() == Type::FloatCon &&
 769       t2->getf() != 0.0 ) // could be negative zero
 770     return TypeF::make( t1->getf()/t2->getf() );
 771 
 772   // If the dividend is a constant zero
 773   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 774   // Test TypeF::ZERO is not sufficient as it could be negative zero
 775 
 776   if( t1 == TypeF::ZERO && !g_isnan(t2->getf()) && t2->getf() != 0.0 )
 777     return TypeF::ZERO;
 778 
 779   // Otherwise we give up all hope
 780   return Type::FLOAT;
 781 }
 782 
 783 //------------------------------isA_Copy---------------------------------------
 784 // Dividing by self is 1.
 785 // If the divisor is 1, we are an identity on the dividend.
 786 Node* DivFNode::Identity(PhaseGVN* phase) {
 787   return (phase->type( in(2) ) == TypeF::ONE) ? in(1) : this;
 788 }
 789 
 790 
 791 //------------------------------Idealize---------------------------------------
 792 Node *DivFNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 793   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 794   // Don't bother trying to transform a dead node
 795   if( in(0) && in(0)->is_top() )  return nullptr;
 796 
 797   const Type *t2 = phase->type( in(2) );
 798   if( t2 == TypeF::ONE )         // Identity?
 799     return nullptr;              // Skip it
 800 
 801   const TypeF *tf = t2->isa_float_constant();
 802   if( !tf ) return nullptr;
 803   if( tf->base() != Type::FloatCon ) return nullptr;
 804 
 805   // Check for out of range values
 806   if( tf->is_nan() || !tf->is_finite() ) return nullptr;
 807 
 808   // Get the value
 809   float f = tf->getf();
 810   int exp;
 811 
 812   // Only for special case of dividing by a power of 2
 813   if( frexp((double)f, &exp) != 0.5 ) return nullptr;
 814 
 815   // Limit the range of acceptable exponents
 816   if( exp < -126 || exp > 126 ) return nullptr;
 817 
 818   // Compute the reciprocal
 819   float reciprocal = ((float)1.0) / f;
 820 
 821   assert( frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
 822 
 823   // return multiplication by the reciprocal
 824   return (new MulFNode(in(1), phase->makecon(TypeF::make(reciprocal))));
 825 }
 826 //=============================================================================
 827 //------------------------------Value------------------------------------------
 828 // An DivHFNode divides its inputs.  The third input is a Control input, used to
 829 // prevent hoisting the divide above an unsafe test.
 830 const Type* DivHFNode::Value(PhaseGVN* phase) const {
 831   // Either input is TOP ==> the result is TOP
 832   const Type* t1 = phase->type(in(1));
 833   const Type* t2 = phase->type(in(2));
 834   if(t1 == Type::TOP) { return Type::TOP; }
 835   if(t2 == Type::TOP) { return Type::TOP; }
 836 
 837   // Either input is BOTTOM ==> the result is the local BOTTOM
 838   const Type* bot = bottom_type();
 839   if((t1 == bot) || (t2 == bot) ||
 840      (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM)) {
 841     return bot;
 842   }
 843 
 844   if (t1->base() == Type::HalfFloatCon &&
 845       t2->base() == Type::HalfFloatCon)  {
 846     // IEEE 754 floating point comparison treats 0.0 and -0.0 as equals.
 847 
 848     // Division of a zero by a zero results in NaN.
 849     if (t1->getf() == 0.0f && t2->getf() == 0.0f) {
 850       return TypeH::make(NAN);
 851     }
 852 
 853     // As per C++ standard section 7.6.5 (expr.mul), behavior is undefined only if
 854     // the second operand is 0.0. In all other situations, we can expect a standard-compliant
 855     // C++ compiler to generate code following IEEE 754 semantics.
 856     if (t2->getf() == 0.0) {
 857       // If either operand is NaN, the result is NaN
 858       if (g_isnan(t1->getf())) {
 859         return TypeH::make(NAN);
 860       } else {
 861         // Division of a nonzero finite value by a zero results in a signed infinity. Also,
 862         // division of an infinity by a finite value results in a signed infinity.
 863         bool res_sign_neg = (jint_cast(t1->getf()) < 0) ^ (jint_cast(t2->getf()) < 0);
 864         const TypeF* res = res_sign_neg ? TypeF::NEG_INF : TypeF::POS_INF;
 865         return TypeH::make(res->getf());
 866       }
 867     }
 868 
 869     return TypeH::make(t1->getf() / t2->getf());
 870   }
 871 
 872   // Otherwise we give up all hope
 873   return Type::HALF_FLOAT;
 874 }
 875 
 876 //-----------------------------------------------------------------------------
 877 // Dividing by self is 1.
 878 // IF the divisor is 1, we are an identity on the dividend.
 879 Node* DivHFNode::Identity(PhaseGVN* phase) {
 880   return (phase->type( in(2) ) == TypeH::ONE) ? in(1) : this;
 881 }
 882 
 883 
 884 //------------------------------Idealize---------------------------------------
 885 Node* DivHFNode::Ideal(PhaseGVN* phase, bool can_reshape) {
 886   if (in(0) != nullptr && remove_dead_region(phase, can_reshape))  return this;
 887   // Don't bother trying to transform a dead node
 888   if (in(0) != nullptr && in(0)->is_top())  { return nullptr; }
 889 
 890   const Type* t2 = phase->type(in(2));
 891   if (t2 == TypeH::ONE) {      // Identity?
 892     return nullptr;            // Skip it
 893   }
 894   const TypeH* tf = t2->isa_half_float_constant();
 895   if(tf == nullptr) { return nullptr; }
 896   if(tf->base() != Type::HalfFloatCon) { return nullptr; }
 897 
 898   // Check for out of range values
 899   if(tf->is_nan() || !tf->is_finite()) { return nullptr; }
 900 
 901   // Get the value
 902   float f = tf->getf();
 903   int exp;
 904 
 905   // Consider the following geometric progression series of POT(power of two) numbers.
 906   // 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,
 907   // In all the above cases, normalized mantissa returned by frexp routine will
 908   // be exactly equal to 0.5 while exponent will be 0,1,2,3...n
 909   // Perform division to multiplication transform only if divisor is a POT value.
 910   if(frexp((double)f, &exp) != 0.5) { return nullptr; }
 911 
 912   // Limit the range of acceptable exponents
 913   if(exp < -14 || exp > 15) { return nullptr; }
 914 
 915   // Since divisor is a POT number, hence its reciprocal will never
 916   // overflow 11 bits precision range of Float16
 917   // value if exponent returned by frexp routine strictly lie
 918   // within the exponent range of normal min(0x1.0P-14) and
 919   // normal max(0x1.ffcP+15) values.
 920   // Thus we can safely compute the reciprocal of divisor without
 921   // any concerns about the precision loss and transform the division
 922   // into a multiplication operation.
 923   float reciprocal = ((float)1.0) / f;
 924 
 925   assert(frexp((double)reciprocal, &exp) == 0.5, "reciprocal should be power of 2");
 926 
 927   // return multiplication by the reciprocal
 928   return (new MulHFNode(in(1), phase->makecon(TypeH::make(reciprocal))));
 929 }
 930 
 931 //=============================================================================
 932 //------------------------------Value------------------------------------------
 933 // An DivDNode divides its inputs.  The third input is a Control input, used to
 934 // prevent hoisting the divide above an unsafe test.
 935 const Type* DivDNode::Value(PhaseGVN* phase) const {
 936   // Either input is TOP ==> the result is TOP
 937   const Type *t1 = phase->type( in(1) );
 938   const Type *t2 = phase->type( in(2) );
 939   if( t1 == Type::TOP ) return Type::TOP;
 940   if( t2 == Type::TOP ) return Type::TOP;
 941 
 942   // Either input is BOTTOM ==> the result is the local BOTTOM
 943   const Type *bot = bottom_type();
 944   if( (t1 == bot) || (t2 == bot) ||
 945       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
 946     return bot;
 947 
 948   // x/x == 1, we ignore 0/0.
 949   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 950   // Does not work for variables because of NaN's
 951   if (in(1) == in(2) && t1->base() == Type::DoubleCon &&
 952       !g_isnan(t1->getd()) && g_isfinite(t1->getd()) && t1->getd() != 0.0) { // could be negative ZERO or NaN
 953     return TypeD::ONE;
 954   }
 955 
 956   if( t2 == TypeD::ONE )
 957     return t1;
 958 
 959   // If divisor is a constant and not zero, divide them numbers
 960   if( t1->base() == Type::DoubleCon &&
 961       t2->base() == Type::DoubleCon &&
 962       t2->getd() != 0.0 ) // could be negative zero
 963     return TypeD::make( t1->getd()/t2->getd() );
 964 
 965   // If the dividend is a constant zero
 966   // Note: if t1 and t2 are zero then result is NaN (JVMS page 213)
 967   // Test TypeF::ZERO is not sufficient as it could be negative zero
 968   if( t1 == TypeD::ZERO && !g_isnan(t2->getd()) && t2->getd() != 0.0 )
 969     return TypeD::ZERO;
 970 
 971   // Otherwise we give up all hope
 972   return Type::DOUBLE;
 973 }
 974 
 975 
 976 //------------------------------isA_Copy---------------------------------------
 977 // Dividing by self is 1.
 978 // If the divisor is 1, we are an identity on the dividend.
 979 Node* DivDNode::Identity(PhaseGVN* phase) {
 980   return (phase->type( in(2) ) == TypeD::ONE) ? in(1) : this;
 981 }
 982 
 983 //------------------------------Idealize---------------------------------------
 984 Node *DivDNode::Ideal(PhaseGVN *phase, bool can_reshape) {
 985   if (in(0) && remove_dead_region(phase, can_reshape))  return this;
 986   // Don't bother trying to transform a dead node
 987   if( in(0) && in(0)->is_top() )  return nullptr;
 988 
 989   const Type *t2 = phase->type( in(2) );
 990   if( t2 == TypeD::ONE )         // Identity?
 991     return nullptr;              // Skip it
 992 
 993   const TypeD *td = t2->isa_double_constant();
 994   if( !td ) return nullptr;
 995   if( td->base() != Type::DoubleCon ) return nullptr;
 996 
 997   // Check for out of range values
 998   if( td->is_nan() || !td->is_finite() ) return nullptr;
 999 
1000   // Get the value
1001   double d = td->getd();
1002   int exp;
1003 
1004   // Only for special case of dividing by a power of 2
1005   if( frexp(d, &exp) != 0.5 ) return nullptr;
1006 
1007   // Limit the range of acceptable exponents
1008   if( exp < -1021 || exp > 1022 ) return nullptr;
1009 
1010   // Compute the reciprocal
1011   double reciprocal = 1.0 / d;
1012 
1013   assert( frexp(reciprocal, &exp) == 0.5, "reciprocal should be power of 2" );
1014 
1015   // return multiplication by the reciprocal
1016   return (new MulDNode(in(1), phase->makecon(TypeD::make(reciprocal))));
1017 }
1018 
1019 //=============================================================================
1020 //------------------------------Identity---------------------------------------
1021 // If the divisor is 1, we are an identity on the dividend.
1022 Node* UDivINode::Identity(PhaseGVN* phase) {
1023   return (phase->type( in(2) )->higher_equal(TypeInt::ONE)) ? in(1) : this;
1024 }
1025 //------------------------------Value------------------------------------------
1026 // A UDivINode divides its inputs.  The third input is a Control input, used to
1027 // prevent hoisting the divide above an unsafe test.
1028 const Type* UDivINode::Value(PhaseGVN* phase) const {
1029   // Either input is TOP ==> the result is TOP
1030   const Type *t1 = phase->type( in(1) );
1031   const Type *t2 = phase->type( in(2) );
1032   if( t1 == Type::TOP ) return Type::TOP;
1033   if( t2 == Type::TOP ) return Type::TOP;
1034 
1035   // x/x == 1 since we always generate the dynamic divisor check for 0.
1036   if (in(1) == in(2)) {
1037     return TypeInt::ONE;
1038   }
1039 
1040   // Either input is BOTTOM ==> the result is the local BOTTOM
1041   const Type *bot = bottom_type();
1042   if( (t1 == bot) || (t2 == bot) ||
1043       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1044     return bot;
1045 
1046   // Otherwise we give up all hope
1047   return TypeInt::INT;
1048 }
1049 
1050 //------------------------------Idealize---------------------------------------
1051 Node *UDivINode::Ideal(PhaseGVN *phase, bool can_reshape) {
1052   return unsigned_div_ideal<TypeInt, juint>(phase, can_reshape, this);
1053 }
1054 
1055 //=============================================================================
1056 //------------------------------Identity---------------------------------------
1057 // If the divisor is 1, we are an identity on the dividend.
1058 Node* UDivLNode::Identity(PhaseGVN* phase) {
1059   return (phase->type( in(2) )->higher_equal(TypeLong::ONE)) ? in(1) : this;
1060 }
1061 //------------------------------Value------------------------------------------
1062 // A UDivLNode divides its inputs.  The third input is a Control input, used to
1063 // prevent hoisting the divide above an unsafe test.
1064 const Type* UDivLNode::Value(PhaseGVN* phase) const {
1065   // Either input is TOP ==> the result is TOP
1066   const Type *t1 = phase->type( in(1) );
1067   const Type *t2 = phase->type( in(2) );
1068   if( t1 == Type::TOP ) return Type::TOP;
1069   if( t2 == Type::TOP ) return Type::TOP;
1070 
1071   // x/x == 1 since we always generate the dynamic divisor check for 0.
1072   if (in(1) == in(2)) {
1073     return TypeLong::ONE;
1074   }
1075 
1076   // Either input is BOTTOM ==> the result is the local BOTTOM
1077   const Type *bot = bottom_type();
1078   if( (t1 == bot) || (t2 == bot) ||
1079       (t1 == Type::BOTTOM) || (t2 == Type::BOTTOM) )
1080     return bot;
1081 
1082   // Otherwise we give up all hope
1083   return TypeLong::LONG;
1084 }
1085 
1086 //------------------------------Idealize---------------------------------------
1087 Node *UDivLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1088   return unsigned_div_ideal<TypeLong, julong>(phase, can_reshape, this);
1089 }
1090 
1091 //=============================================================================
1092 //------------------------------Idealize---------------------------------------
1093 Node *ModINode::Ideal(PhaseGVN *phase, bool can_reshape) {
1094   // Check for dead control input
1095   if( in(0) && remove_dead_region(phase, can_reshape) )  return this;
1096   // Don't bother trying to transform a dead node
1097   if( in(0) && in(0)->is_top() )  return nullptr;
1098 
1099   // Get the modulus
1100   const Type *t = phase->type( in(2) );
1101   if( t == Type::TOP ) return nullptr;
1102   const TypeInt *ti = t->is_int();
1103 
1104   // Check for useless control input
1105   // Check for excluding mod-zero case
1106   if (in(0) && (ti->_hi < 0 || ti->_lo > 0)) {
1107     set_req(0, nullptr);        // Yank control input
1108     return this;
1109   }
1110 
1111   // See if we are MOD'ing by 2^k or 2^k-1.
1112   if( !ti->is_con() ) return nullptr;
1113   jint con = ti->get_con();
1114 
1115   Node *hook = new Node(1);
1116 
1117   // First, special check for modulo 2^k-1
1118   if( con >= 0 && con < max_jint && is_power_of_2(con+1) ) {
1119     uint k = exact_log2(con+1);  // Extract k
1120 
1121     // Basic algorithm by David Detlefs.  See fastmod_int.java for gory details.
1122     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*/};
1123     int trip_count = 1;
1124     if( k < ARRAY_SIZE(unroll_factor))  trip_count = unroll_factor[k];
1125 
1126     // If the unroll factor is not too large, and if conditional moves are
1127     // ok, then use this case
1128     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1129       Node *x = in(1);            // Value being mod'd
1130       Node *divisor = in(2);      // Also is mask
1131 
1132       hook->init_req(0, x);       // Add a use to x to prevent him from dying
1133       // Generate code to reduce X rapidly to nearly 2^k-1.
1134       for( int i = 0; i < trip_count; i++ ) {
1135         Node *xl = phase->transform( new AndINode(x,divisor) );
1136         Node *xh = phase->transform( new RShiftINode(x,phase->intcon(k)) ); // Must be signed
1137         x = phase->transform( new AddINode(xh,xl) );
1138         hook->set_req(0, x);
1139       }
1140 
1141       // Generate sign-fixup code.  Was original value positive?
1142       // int hack_res = (i >= 0) ? divisor : 1;
1143       Node *cmp1 = phase->transform( new CmpINode( in(1), phase->intcon(0) ) );
1144       Node *bol1 = phase->transform( new BoolNode( cmp1, BoolTest::ge ) );
1145       Node *cmov1= phase->transform( new CMoveINode(bol1, phase->intcon(1), divisor, TypeInt::POS) );
1146       // if( x >= hack_res ) x -= divisor;
1147       Node *sub  = phase->transform( new SubINode( x, divisor ) );
1148       Node *cmp2 = phase->transform( new CmpINode( x, cmov1 ) );
1149       Node *bol2 = phase->transform( new BoolNode( cmp2, BoolTest::ge ) );
1150       // Convention is to not transform the return value of an Ideal
1151       // since Ideal is expected to return a modified 'this' or a new node.
1152       Node *cmov2= new CMoveINode(bol2, x, sub, TypeInt::INT);
1153       // cmov2 is now the mod
1154 
1155       // Now remove the bogus extra edges used to keep things alive
1156       hook->destruct(phase);
1157       return cmov2;
1158     }
1159   }
1160 
1161   // Fell thru, the unroll case is not appropriate. Transform the modulo
1162   // into a long multiply/int multiply/subtract case
1163 
1164   // Cannot handle mod 0, and min_jint isn't handled by the transform
1165   if( con == 0 || con == min_jint ) return nullptr;
1166 
1167   // Get the absolute value of the constant; at this point, we can use this
1168   jint pos_con = (con >= 0) ? con : -con;
1169 
1170   // integer Mod 1 is always 0
1171   if( pos_con == 1 ) return new ConINode(TypeInt::ZERO);
1172 
1173   int log2_con = -1;
1174 
1175   // If this is a power of two, they maybe we can mask it
1176   if (is_power_of_2(pos_con)) {
1177     log2_con = log2i_exact(pos_con);
1178 
1179     const Type *dt = phase->type(in(1));
1180     const TypeInt *dti = dt->isa_int();
1181 
1182     // See if this can be masked, if the dividend is non-negative
1183     if( dti && dti->_lo >= 0 )
1184       return ( new AndINode( in(1), phase->intcon( pos_con-1 ) ) );
1185   }
1186 
1187   // Save in(1) so that it cannot be changed or deleted
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   Node *hook = new Node(1);
1411 
1412   // Expand mod
1413   if(con >= 0 && con < max_jlong && is_power_of_2(con + 1)) {
1414     uint k = log2i_exact(con + 1);  // Extract k
1415 
1416     // Basic algorithm by David Detlefs.  See fastmod_long.java for gory details.
1417     // Used to help a popular random number generator which does a long-mod
1418     // of 2^31-1 and shows up in SpecJBB and SciMark.
1419     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*/};
1420     int trip_count = 1;
1421     if( k < ARRAY_SIZE(unroll_factor)) trip_count = unroll_factor[k];
1422 
1423     // If the unroll factor is not too large, and if conditional moves are
1424     // ok, then use this case
1425     if( trip_count <= 5 && ConditionalMoveLimit != 0 ) {
1426       Node *x = in(1);            // Value being mod'd
1427       Node *divisor = in(2);      // Also is mask
1428 
1429       hook->init_req(0, x);       // Add a use to x to prevent him from dying
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 him 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   hook->init_req(0, in(1));
1486 
1487   // Divide using the transform from DivL to MulL
1488   Node *result = transform_long_divide( phase, in(1), pos_con );
1489   if (result != nullptr) {
1490     Node *divide = phase->transform(result);
1491 
1492     // Re-multiply, using a shift if this is a power of two
1493     Node *mult = nullptr;
1494 
1495     if( log2_con >= 0 )
1496       mult = phase->transform( new LShiftLNode( divide, phase->intcon( log2_con ) ) );
1497     else
1498       mult = phase->transform( new MulLNode( divide, phase->longcon( pos_con ) ) );
1499 
1500     // Finally, subtract the multiplied divided value from the original
1501     result = new SubLNode( in(1), mult );
1502   }
1503 
1504   // Now remove the bogus extra edges used to keep things alive
1505   hook->destruct(phase);
1506 
1507   // return the value
1508   return result;
1509 }
1510 
1511 //------------------------------Value------------------------------------------
1512 const Type* ModLNode::Value(PhaseGVN* phase) const {
1513   return mod_value(phase, in(1), in(2), T_LONG);
1514 }
1515 
1516 Node *UModLNode::Ideal(PhaseGVN *phase, bool can_reshape) {
1517   return unsigned_mod_ideal<TypeLong, julong>(phase, can_reshape, this);
1518 }
1519 
1520 const Type* UModLNode::Value(PhaseGVN* phase) const {
1521   return unsigned_mod_value<TypeLong, julong, jlong>(phase, this);
1522 }
1523 
1524 const Type* ModFNode::get_result_if_constant(const Type* dividend, const Type* divisor) const {
1525   // If either number is not a constant, we know nothing.
1526   if ((dividend->base() != Type::FloatCon) || (divisor->base() != Type::FloatCon)) {
1527     return nullptr; // note: x%x can be either NaN or 0
1528   }
1529 
1530   float dividend_f = dividend->getf();
1531   float divisor_f = divisor->getf();
1532   jint dividend_i = jint_cast(dividend_f); // note:  *(int*)&f1, not just (int)f1
1533   jint divisor_i = jint_cast(divisor_f);
1534 
1535   // If either is a NaN, return an input NaN
1536   if (g_isnan(dividend_f)) {
1537     return dividend;
1538   }
1539   if (g_isnan(divisor_f)) {
1540     return divisor;
1541   }
1542 
1543   // If an operand is infinity or the divisor is +/- zero, punt.
1544   if (!g_isfinite(dividend_f) || !g_isfinite(divisor_f) || divisor_i == 0 || divisor_i == min_jint) {
1545     return nullptr;
1546   }
1547 
1548   // We must be modulo'ing 2 float constants.
1549   // Make sure that the sign of the fmod is equal to the sign of the dividend
1550   jint xr = jint_cast(fmod(dividend_f, divisor_f));
1551   if ((dividend_i ^ xr) < 0) {
1552     xr ^= min_jint;
1553   }
1554 
1555   return TypeF::make(jfloat_cast(xr));
1556 }
1557 
1558 const Type* ModDNode::get_result_if_constant(const Type* dividend, const Type* divisor) const {
1559   // If either number is not a constant, we know nothing.
1560   if ((dividend->base() != Type::DoubleCon) || (divisor->base() != Type::DoubleCon)) {
1561     return nullptr; // note: x%x can be either NaN or 0
1562   }
1563 
1564   double dividend_d = dividend->getd();
1565   double divisor_d = divisor->getd();
1566   jlong dividend_l = jlong_cast(dividend_d); // note:  *(long*)&f1, not just (long)f1
1567   jlong divisor_l = jlong_cast(divisor_d);
1568 
1569   // If either is a NaN, return an input NaN
1570   if (g_isnan(dividend_d)) {
1571     return dividend;
1572   }
1573   if (g_isnan(divisor_d)) {
1574     return divisor;
1575   }
1576 
1577   // If an operand is infinity or the divisor is +/- zero, punt.
1578   if (!g_isfinite(dividend_d) || !g_isfinite(divisor_d) || divisor_l == 0 || divisor_l == min_jlong) {
1579     return nullptr;
1580   }
1581 
1582   // We must be modulo'ing 2 double constants.
1583   // Make sure that the sign of the fmod is equal to the sign of the dividend
1584   jlong xr = jlong_cast(fmod(dividend_d, divisor_d));
1585   if ((dividend_l ^ xr) < 0) {
1586     xr ^= min_jlong;
1587   }
1588 
1589   return TypeD::make(jdouble_cast(xr));
1590 }
1591 
1592 Node* ModFloatingNode::Ideal(PhaseGVN* phase, bool can_reshape) {
1593   if (can_reshape) {
1594     PhaseIterGVN* igvn = phase->is_IterGVN();
1595 
1596     // Either input is TOP ==> the result is 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 phase->C->top();
1601     }
1602     const Type* constant_result = get_result_if_constant(dividend_type, divisor_type);
1603     if (constant_result != nullptr) {
1604       return make_tuple_of_input_state_and_constant_result(igvn, constant_result);
1605     }
1606   }
1607 
1608   return CallLeafPureNode::Ideal(phase, can_reshape);
1609 }
1610 
1611 /* Give a tuple node for ::Ideal to return, made of the input state (control to return addr)
1612  * and the given constant result. Idealization of projections will make sure to transparently
1613  * propagate the input state and replace the result by the said constant.
1614  */
1615 TupleNode* ModFloatingNode::make_tuple_of_input_state_and_constant_result(PhaseIterGVN* phase, const Type* con) const {
1616   Node* con_node = phase->makecon(con);
1617   TupleNode* tuple = TupleNode::make(
1618       tf()->range_cc(),
1619       in(TypeFunc::Control),
1620       in(TypeFunc::I_O),
1621       in(TypeFunc::Memory),
1622       in(TypeFunc::FramePtr),
1623       in(TypeFunc::ReturnAdr),
1624       con_node);
1625 
1626   return tuple;
1627 }
1628 
1629 //=============================================================================
1630 
1631 DivModNode::DivModNode( Node *c, Node *dividend, Node *divisor ) : MultiNode(3) {
1632   init_req(0, c);
1633   init_req(1, dividend);
1634   init_req(2, divisor);
1635 }
1636 
1637 DivModNode* DivModNode::make(Node* div_or_mod, BasicType bt, bool is_unsigned) {
1638   assert(bt == T_INT || bt == T_LONG, "only int or long input pattern accepted");
1639 
1640   if (bt == T_INT) {
1641     if (is_unsigned) {
1642       return UDivModINode::make(div_or_mod);
1643     } else {
1644       return DivModINode::make(div_or_mod);
1645     }
1646   } else {
1647     if (is_unsigned) {
1648       return UDivModLNode::make(div_or_mod);
1649     } else {
1650       return DivModLNode::make(div_or_mod);
1651     }
1652   }
1653 }
1654 
1655 //------------------------------make------------------------------------------
1656 DivModINode* DivModINode::make(Node* div_or_mod) {
1657   Node* n = div_or_mod;
1658   assert(n->Opcode() == Op_DivI || n->Opcode() == Op_ModI,
1659          "only div or mod input pattern accepted");
1660 
1661   DivModINode* divmod = new DivModINode(n->in(0), n->in(1), n->in(2));
1662   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1663   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1664   return divmod;
1665 }
1666 
1667 //------------------------------make------------------------------------------
1668 DivModLNode* DivModLNode::make(Node* div_or_mod) {
1669   Node* n = div_or_mod;
1670   assert(n->Opcode() == Op_DivL || n->Opcode() == Op_ModL,
1671          "only div or mod input pattern accepted");
1672 
1673   DivModLNode* divmod = new DivModLNode(n->in(0), n->in(1), n->in(2));
1674   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1675   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1676   return divmod;
1677 }
1678 
1679 //------------------------------match------------------------------------------
1680 // return result(s) along with their RegMask info
1681 Node *DivModINode::match(const ProjNode *proj, const Matcher *match, const RegMask* mask) {
1682   uint ideal_reg = proj->ideal_reg();
1683   RegMask rm;
1684   if (proj->_con == div_proj_num) {
1685     rm.assignFrom(match->divI_proj_mask());
1686   } else {
1687     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1688     rm.assignFrom(match->modI_proj_mask());
1689   }
1690   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1691 }
1692 
1693 
1694 //------------------------------match------------------------------------------
1695 // return result(s) along with their RegMask info
1696 Node *DivModLNode::match(const ProjNode *proj, const Matcher *match, const RegMask* mask) {
1697   uint ideal_reg = proj->ideal_reg();
1698   RegMask rm;
1699   if (proj->_con == div_proj_num) {
1700     rm.assignFrom(match->divL_proj_mask());
1701   } else {
1702     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1703     rm.assignFrom(match->modL_proj_mask());
1704   }
1705   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1706 }
1707 
1708 //------------------------------make------------------------------------------
1709 UDivModINode* UDivModINode::make(Node* div_or_mod) {
1710   Node* n = div_or_mod;
1711   assert(n->Opcode() == Op_UDivI || n->Opcode() == Op_UModI,
1712          "only div or mod input pattern accepted");
1713 
1714   UDivModINode* divmod = new UDivModINode(n->in(0), n->in(1), n->in(2));
1715   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1716   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1717   return divmod;
1718 }
1719 
1720 //------------------------------make------------------------------------------
1721 UDivModLNode* UDivModLNode::make(Node* div_or_mod) {
1722   Node* n = div_or_mod;
1723   assert(n->Opcode() == Op_UDivL || n->Opcode() == Op_UModL,
1724          "only div or mod input pattern accepted");
1725 
1726   UDivModLNode* divmod = new UDivModLNode(n->in(0), n->in(1), n->in(2));
1727   Node*        dproj  = new ProjNode(divmod, DivModNode::div_proj_num);
1728   Node*        mproj  = new ProjNode(divmod, DivModNode::mod_proj_num);
1729   return divmod;
1730 }
1731 
1732 //------------------------------match------------------------------------------
1733 // return result(s) along with their RegMask info
1734 Node* UDivModINode::match(const ProjNode* proj, const Matcher* match, const RegMask* mask) {
1735   uint ideal_reg = proj->ideal_reg();
1736   RegMask rm;
1737   if (proj->_con == div_proj_num) {
1738     rm.assignFrom(match->divI_proj_mask());
1739   } else {
1740     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1741     rm.assignFrom(match->modI_proj_mask());
1742   }
1743   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1744 }
1745 
1746 
1747 //------------------------------match------------------------------------------
1748 // return result(s) along with their RegMask info
1749 Node* UDivModLNode::match( const ProjNode* proj, const Matcher* match, const RegMask* mask) {
1750   uint ideal_reg = proj->ideal_reg();
1751   RegMask rm;
1752   if (proj->_con == div_proj_num) {
1753     rm.assignFrom(match->divL_proj_mask());
1754   } else {
1755     assert(proj->_con == mod_proj_num, "must be div or mod projection");
1756     rm.assignFrom(match->modL_proj_mask());
1757   }
1758   return new MachProjNode(this, proj->_con, rm, ideal_reg);
1759 }