Merge

hotspot/make/linux/makefiles/gcc.make

@@ -350,9 +350,9 @@ else
   ifeq ($(DEBUG_CFLAGS/$(BUILDARCH)),)
       ifeq ($(USE_CLANG), true)
         # Clang doesn't understand -gstabs
-        OPT_CFLAGS += -g
+        DEBUG_CFLAGS += -g
       else
-        OPT_CFLAGS += -gstabs
+        DEBUG_CFLAGS += -gstabs
       endif
   endif
   
@@ -365,9 +365,9 @@ else
     ifeq ($(FASTDEBUG_CFLAGS/$(BUILDARCH)),)
       ifeq ($(USE_CLANG), true)
         # Clang doesn't understand -gstabs
-        OPT_CFLAGS += -g
+        FASTDEBUG_CFLAGS += -g
       else
-        OPT_CFLAGS += -gstabs
+        FASTDEBUG_CFLAGS += -gstabs
       endif
     endif
   

hotspot/src/cpu/sparc/vm/macroAssembler_sparc.cpp

@@ -1161,12 +1161,6 @@ void MacroAssembler::align(int modulus) {
   while (offset() % modulus != 0) nop();
 }
 
-
-void MacroAssembler::safepoint() {
-  relocate(breakpoint_Relocation::spec(breakpoint_Relocation::safepoint));
-}
-
-
 void RegistersForDebugging::print(outputStream* s) {
   FlagSetting fs(Debugging, true);
   int j;

hotspot/src/cpu/sparc/vm/relocInfo_sparc.cpp

@@ -193,36 +193,6 @@ address Relocation::pd_get_address_from_code() {
   return *(address*)addr();
 }
 
-
-int Relocation::pd_breakpoint_size() {
-  // minimum breakpoint size, in short words
-  return NativeIllegalInstruction::instruction_size / sizeof(short);
-}
-
-void Relocation::pd_swap_in_breakpoint(address x, short* instrs, int instrlen) {
-  Untested("pd_swap_in_breakpoint");
-  // %%% probably do not need a general instrlen; just use the trap size
-  if (instrs != NULL) {
-    assert(instrlen * sizeof(short) == NativeIllegalInstruction::instruction_size, "enough instrlen in reloc. data");
-    for (int i = 0; i < instrlen; i++) {
-      instrs[i] = ((short*)x)[i];
-    }
-  }
-  NativeIllegalInstruction::insert(x);
-}
-
-
-void Relocation::pd_swap_out_breakpoint(address x, short* instrs, int instrlen) {
-  Untested("pd_swap_out_breakpoint");
-  assert(instrlen * sizeof(short) == sizeof(int), "enough buf");
-  union { int l; short s[1]; } u;
-  for (int i = 0; i < instrlen; i++) {
-    u.s[i] = instrs[i];
-  }
-  NativeInstruction* ni = nativeInstruction_at(x);
-  ni->set_long_at(0, u.l);
-}
-
 void poll_Relocation::fix_relocation_after_move(const CodeBuffer* src, CodeBuffer* dest) {
 }
 

hotspot/src/cpu/x86/vm/relocInfo_x86.cpp

@@ -177,30 +177,6 @@ address Relocation::pd_get_address_from_code() {
   return *pd_address_in_code();
 }
 
-int Relocation::pd_breakpoint_size() {
-  // minimum breakpoint size, in short words
-  return NativeIllegalInstruction::instruction_size / sizeof(short);
-}
-
-void Relocation::pd_swap_in_breakpoint(address x, short* instrs, int instrlen) {
-  Untested("pd_swap_in_breakpoint");
-  if (instrs != NULL) {
-    assert(instrlen * sizeof(short) == NativeIllegalInstruction::instruction_size, "enough instrlen in reloc. data");
-    for (int i = 0; i < instrlen; i++) {
-      instrs[i] = ((short*)x)[i];
-    }
-  }
-  NativeIllegalInstruction::insert(x);
-}
-
-
-void Relocation::pd_swap_out_breakpoint(address x, short* instrs, int instrlen) {
-  Untested("pd_swap_out_breakpoint");
-  assert(NativeIllegalInstruction::instruction_size == sizeof(short), "right address unit for update");
-  NativeInstruction* ni = nativeInstruction_at(x);
-  *(short*)ni->addr_at(0) = instrs[0];
-}
-
 void poll_Relocation::fix_relocation_after_move(const CodeBuffer* src, CodeBuffer* dest) {
 #ifdef _LP64
   if (!Assembler::is_polling_page_far()) {

hotspot/src/cpu/zero/vm/relocInfo_zero.cpp

@@ -52,22 +52,6 @@ address* Relocation::pd_address_in_code() {
   return (address *) addr();
 }
 
-int Relocation::pd_breakpoint_size() {
-  ShouldNotCallThis();
-}
-
-void Relocation::pd_swap_in_breakpoint(address x,
-                                       short*  instrs,
-                                       int     instrlen) {
-  ShouldNotCallThis();
-}
-
-void Relocation::pd_swap_out_breakpoint(address x,
-                                        short*  instrs,
-                                        int     instrlen) {
-  ShouldNotCallThis();
-}
-
 void poll_Relocation::fix_relocation_after_move(const CodeBuffer* src,
                                                 CodeBuffer*       dst) {
   ShouldNotCallThis();

hotspot/src/share/vm/code/nmethod.cpp

@@ -1081,11 +1081,6 @@ void nmethod::fix_oop_relocations(address begin, address end, bool initialize_im
       metadata_Relocation* reloc = iter.metadata_reloc();
       reloc->fix_metadata_relocation();
     }
-
-    // There must not be any interfering patches or breakpoints.
-    assert(!(iter.type() == relocInfo::breakpoint_type
-             && iter.breakpoint_reloc()->active()),
-           "no active breakpoint");
   }
 }
 

hotspot/src/share/vm/code/relocInfo.cpp

@@ -338,31 +338,6 @@ void RelocIterator::set_limit(address limit) {
   _limit = limit;
 }
 
-
-void PatchingRelocIterator:: prepass() {
-  // turn breakpoints off during patching
-  _init_state = (*this);        // save cursor
-  while (next()) {
-    if (type() == relocInfo::breakpoint_type) {
-      breakpoint_reloc()->set_active(false);
-    }
-  }
-  (RelocIterator&)(*this) = _init_state;        // reset cursor for client
-}
-
-
-void PatchingRelocIterator:: postpass() {
-  // turn breakpoints back on after patching
-  (RelocIterator&)(*this) = _init_state;        // reset cursor again
-  while (next()) {
-    if (type() == relocInfo::breakpoint_type) {
-      breakpoint_Relocation* bpt = breakpoint_reloc();
-      bpt->set_active(bpt->enabled());
-    }
-  }
-}
-
-
 // All the strange bit-encodings are in here.
 // The idea is to encode relocation data which are small integers
 // very efficiently (a single extra halfword).  Larger chunks of
@@ -704,51 +679,6 @@ void section_word_Relocation::unpack_data() {
   _target  = address_from_scaled_offset(offset, base);
 }
 
-
-void breakpoint_Relocation::pack_data_to(CodeSection* dest) {
-  short* p = (short*) dest->locs_end();
-  address point = dest->locs_point();
-
-  *p++ = _bits;
-
-  assert(_target != NULL, "sanity");
-
-  if (internal())  normalize_address(_target, dest);
-
-  jint target_bits =
-    (jint)( internal() ? scaled_offset           (_target, point)
-                       : runtime_address_to_index(_target) );
-  if (settable()) {
-    // save space for set_target later
-    p = add_jint(p, target_bits);
-  } else {
-    p = add_var_int(p, target_bits);
-  }
-
-  for (int i = 0; i < instrlen(); i++) {
-    // put placeholder words until bytes can be saved
-    p = add_short(p, (short)0x7777);
-  }
-
-  dest->set_locs_end((relocInfo*) p);
-}
-
-
-void breakpoint_Relocation::unpack_data() {
-  _bits = live_bits();
-
-  int targetlen = datalen() - 1 - instrlen();
-  jint target_bits = 0;
-  if (targetlen == 0)       target_bits = 0;
-  else if (targetlen == 1)  target_bits = *(data()+1);
-  else if (targetlen == 2)  target_bits = relocInfo::jint_from_data(data()+1);
-  else                      { ShouldNotReachHere(); }
-
-  _target = internal() ? address_from_scaled_offset(target_bits, addr())
-                       : index_to_runtime_address  (target_bits);
-}
-
-
 //// miscellaneous methods
 oop* oop_Relocation::oop_addr() {
   int n = _oop_index;
@@ -933,81 +863,6 @@ address internal_word_Relocation::target() {
   return target;
 }
 
-
-breakpoint_Relocation::breakpoint_Relocation(int kind, address target, bool internal) {
-  bool active    = false;
-  bool enabled   = (kind == initialization);
-  bool removable = (kind != safepoint);
-  bool settable  = (target == NULL);
-
-  int bits = kind;
-  if (enabled)    bits |= enabled_state;
-  if (internal)   bits |= internal_attr;
-  if (removable)  bits |= removable_attr;
-  if (settable)   bits |= settable_attr;
-
-  _bits = bits | high_bit;
-  _target = target;
-
-  assert(this->kind()      == kind,      "kind encoded");
-  assert(this->enabled()   == enabled,   "enabled encoded");
-  assert(this->active()    == active,    "active encoded");
-  assert(this->internal()  == internal,  "internal encoded");
-  assert(this->removable() == removable, "removable encoded");
-  assert(this->settable()  == settable,  "settable encoded");
-}
-
-
-address breakpoint_Relocation::target() const {
-  return _target;
-}
-
-
-void breakpoint_Relocation::set_target(address x) {
-  assert(settable(), "must be settable");
-  jint target_bits =
-    (jint)(internal() ? scaled_offset           (x, addr())
-                      : runtime_address_to_index(x));
-  short* p = &live_bits() + 1;
-  p = add_jint(p, target_bits);
-  assert(p == instrs(), "new target must fit");
-  _target = x;
-}
-
-
-void breakpoint_Relocation::set_enabled(bool b) {
-  if (enabled() == b) return;
-
-  if (b) {
-    set_bits(bits() | enabled_state);
-  } else {
-    set_active(false);          // remove the actual breakpoint insn, if any
-    set_bits(bits() & ~enabled_state);
-  }
-}
-
-
-void breakpoint_Relocation::set_active(bool b) {
-  assert(!b || enabled(), "cannot activate a disabled breakpoint");
-
-  if (active() == b) return;
-
-  // %%% should probably seize a lock here (might not be the right lock)
-  //MutexLockerEx ml_patch(Patching_lock, true);
-  //if (active() == b)  return;         // recheck state after locking
-
-  if (b) {
-    set_bits(bits() | active_state);
-    if (instrlen() == 0)
-      fatal("breakpoints in original code must be undoable");
-    pd_swap_in_breakpoint (addr(), instrs(), instrlen());
-  } else {
-    set_bits(bits() & ~active_state);
-    pd_swap_out_breakpoint(addr(), instrs(), instrlen());
-  }
-}
-
-
 //---------------------------------------------------------------------------------
 // Non-product code
 

hotspot/src/share/vm/code/relocInfo.hpp

@@ -49,9 +49,6 @@ class NativeMovConstReg;
 //    RelocIterator
 //      A StackObj which iterates over the relocations associated with
 //      a range of code addresses.  Can be used to operate a copy of code.
-//    PatchingRelocIterator
-//      Specialized subtype of RelocIterator which removes breakpoints
-//      temporarily during iteration, then restores them.
 //    BoundRelocation
 //      An _internal_ type shared by packers and unpackers of relocations.
 //      It pastes together a RelocationHolder with some pointers into
@@ -204,15 +201,6 @@ class NativeMovConstReg;
 //   immediate field must not straddle a unit of memory coherence.
 //   //%note reloc_3
 //
-// relocInfo::breakpoint_type -- a conditional breakpoint in the code
-//   Value:  none
-//   Instruction types: any whatsoever
-//   Data:  [b [T]t  i...]
-//   The b is a bit-packed word representing the breakpoint's attributes.
-//   The t is a target address which the breakpoint calls (when it is enabled).
-//   The i... is a place to store one or two instruction words overwritten
-//   by a trap, so that the breakpoint may be subsequently removed.
-//
 // relocInfo::static_stub_type -- an extra stub for each static_call_type
 //   Value:  none
 //   Instruction types: a virtual call:  { set_oop; jump; }
@@ -271,8 +259,8 @@ class relocInfo VALUE_OBJ_CLASS_SPEC {
     section_word_type       =  9, // internal, but a cross-section reference
     poll_type               = 10, // polling instruction for safepoints
     poll_return_type        = 11, // polling instruction for safepoints at return
-    breakpoint_type         = 12, // an initialization barrier or safepoint
+    metadata_type           = 12, // metadata that used to be oops
-    metadata_type           = 13, // metadata that used to be oops
+    yet_unused_type_1       = 13, // Still unused
     yet_unused_type_2       = 14, // Still unused
     data_prefix_tag         = 15, // tag for a prefix (carries data arguments)
     type_mask               = 15  // A mask which selects only the above values
@@ -312,7 +300,6 @@ class relocInfo VALUE_OBJ_CLASS_SPEC {
     visitor(internal_word) \
     visitor(poll) \
     visitor(poll_return) \
-    visitor(breakpoint) \
     visitor(section_word) \
 
 
@@ -454,7 +441,7 @@ class relocInfo VALUE_OBJ_CLASS_SPEC {
  public:
   enum {
     // Conservatively large estimate of maximum length (in shorts)
-    // of any relocation record (probably breakpoints are largest).
+    // of any relocation record.
     // Extended format is length prefix, data words, and tag/offset suffix.
     length_limit       = 1 + 1 + (3*BytesPerWord/BytesPerShort) + 1,
     have_format        = format_width > 0
@@ -571,8 +558,6 @@ class RelocIterator : public StackObj {
 
   void initialize(nmethod* nm, address begin, address limit);
 
-  friend class PatchingRelocIterator;
-  // make an uninitialized one, for PatchingRelocIterator:
   RelocIterator() { initialize_misc(); }
 
  public:
@@ -779,9 +764,6 @@ class Relocation VALUE_OBJ_CLASS_SPEC {
   void       pd_verify_data_value    (address x, intptr_t off) { pd_set_data_value(x, off, true); }
   address    pd_call_destination     (address orig_addr = NULL);
   void       pd_set_call_destination (address x);
-  void       pd_swap_in_breakpoint   (address x, short* instrs, int instrlen);
-  void       pd_swap_out_breakpoint  (address x, short* instrs, int instrlen);
-  static int pd_breakpoint_size      ();
 
   // this extracts the address of an address in the code stream instead of the reloc data
   address* pd_address_in_code       ();
@@ -1302,87 +1284,6 @@ class poll_return_Relocation : public Relocation {
   void     fix_relocation_after_move(const CodeBuffer* src, CodeBuffer* dest);
 };
 
-
-class breakpoint_Relocation : public Relocation {
-  relocInfo::relocType type() { return relocInfo::breakpoint_type; }
-
-  enum {
-    // attributes which affect the interpretation of the data:
-    removable_attr = 0x0010,   // buffer [i...] allows for undoing the trap
-    internal_attr  = 0x0020,   // the target is an internal addr (local stub)
-    settable_attr  = 0x0040,   // the target is settable
-
-    // states which can change over time:
-    enabled_state  = 0x0100,   // breakpoint must be active in running code
-    active_state   = 0x0200,   // breakpoint instruction actually in code
-
-    kind_mask      = 0x000F,   // mask for extracting kind
-    high_bit       = 0x4000    // extra bit which is always set
-  };
-
- public:
-  enum {
-    // kinds:
-    initialization = 1,
-    safepoint      = 2
-  };
-
-  // If target is NULL, 32 bits are reserved for a later set_target().
-  static RelocationHolder spec(int kind, address target = NULL, bool internal_target = false) {
-    RelocationHolder rh = newHolder();
-    new(rh) breakpoint_Relocation(kind, target, internal_target);
-    return rh;
-  }
-
- private:
-  // We require every bits value to NOT to fit into relocInfo::datalen_width,
-  // because we are going to actually store state in the reloc, and so
-  // cannot allow it to be compressed (and hence copied by the iterator).
-
-  short   _bits;                  // bit-encoded kind, attrs, & state
-  address _target;
-
-  breakpoint_Relocation(int kind, address target, bool internal_target);
-
-  friend class RelocIterator;
-  breakpoint_Relocation() { }
-
-  short    bits()       const { return _bits; }
-  short&   live_bits()  const { return data()[0]; }
-  short*   instrs()     const { return data() + datalen() - instrlen(); }
-  int      instrlen()   const { return removable() ? pd_breakpoint_size() : 0; }
-
-  void set_bits(short x) {
-    assert(live_bits() == _bits, "must be the only mutator of reloc info");
-    live_bits() = _bits = x;
-  }
-
- public:
-  address  target()     const;
-  void set_target(address x);
-
-  int  kind()           const { return  bits() & kind_mask; }
-  bool enabled()        const { return (bits() &  enabled_state) != 0; }
-  bool active()         const { return (bits() &   active_state) != 0; }
-  bool internal()       const { return (bits() &  internal_attr) != 0; }
-  bool removable()      const { return (bits() & removable_attr) != 0; }
-  bool settable()       const { return (bits() &  settable_attr) != 0; }
-
-  void set_enabled(bool b);     // to activate, you must also say set_active
-  void set_active(bool b);      // actually inserts bpt (must be enabled 1st)
-
-  // data is packed as 16 bits, followed by the target (1 or 2 words), followed
-  // if necessary by empty storage for saving away original instruction bytes.
-  void pack_data_to(CodeSection* dest);
-  void unpack_data();
-
-  // during certain operations, breakpoints must be out of the way:
-  void fix_relocation_after_move(const CodeBuffer* src, CodeBuffer* dest) {
-    assert(!active(), "cannot perform relocation on enabled breakpoints");
-  }
-};
-
-
 // We know all the xxx_Relocation classes, so now we can define these:
 #define EACH_CASE(name)                                         \
 inline name##_Relocation* RelocIterator::name##_reloc() {       \
@@ -1401,25 +1302,4 @@ inline RelocIterator::RelocIterator(nmethod* nm, address begin, address limit) {
   initialize(nm, begin, limit);
 }
 
-// if you are going to patch code, you should use this subclass of
-// RelocIterator
-class PatchingRelocIterator : public RelocIterator {
- private:
-  RelocIterator _init_state;
-
-  void prepass();               // deactivates all breakpoints
-  void postpass();              // reactivates all enabled breakpoints
-
-  // do not copy these puppies; it would have unpredictable side effects
-  // these are private and have no bodies defined because they should not be called
-  PatchingRelocIterator(const RelocIterator&);
-  void        operator=(const RelocIterator&);
-
- public:
-  PatchingRelocIterator(nmethod* nm, address begin = NULL, address limit = NULL)
-    : RelocIterator(nm, begin, limit)                { prepass();  }
-
-  ~PatchingRelocIterator()                           { postpass(); }
-};
-
 #endif // SHARE_VM_CODE_RELOCINFO_HPP

hotspot/src/share/vm/interpreter/bytecodeInterpreter.cpp

@@ -481,9 +481,9 @@ BytecodeInterpreter::run(interpreterState istate) {
     // So we have a second version of the assertion which handles the case where EnableInvokeDynamic was
     // switched off because of the wrong classes.
     if (EnableInvokeDynamic || FLAG_IS_CMDLINE(EnableInvokeDynamic)) {
-      assert(abs(istate->_stack_base - istate->_stack_limit) == (istate->_method->max_stack() + 1), "bad stack limit");
+      assert(labs(istate->_stack_base - istate->_stack_limit) == (istate->_method->max_stack() + 1), "bad stack limit");
     } else {
-      const int extra_stack_entries = Method::extra_stack_entries_for_indy;
+      const int extra_stack_entries = Method::extra_stack_entries_for_jsr292;
       assert(labs(istate->_stack_base - istate->_stack_limit) == (istate->_method->max_stack() + extra_stack_entries
                                                                                                + 1), "bad stack limit");
     }
@@ -2233,7 +2233,7 @@ run:
         }
 
         Method* method = cache->f1_as_method();
-        VERIFY_OOP(method);
+        if (VerifyOops) method->verify();
 
         if (cache->has_appendix()) {
           ConstantPool* constants = METHOD->constants();
@@ -2265,8 +2265,7 @@ run:
         }
 
         Method* method = cache->f1_as_method();
-
+        if (VerifyOops) method->verify();
-        VERIFY_OOP(method);
 
         if (cache->has_appendix()) {
           ConstantPool* constants = METHOD->constants();

hotspot/src/share/vm/opto/memnode.cpp

@@ -2943,12 +2943,20 @@ Node *MemBarNode::Ideal(PhaseGVN *phase, bool can_reshape) {
       Node* my_mem = in(MemBarNode::Precedent);
       // The MembarAquire may keep an unused LoadNode alive through the Precedent edge
       if ((my_mem != NULL) && (opc == Op_MemBarAcquire) && (my_mem->outcnt() == 1)) {
+        // if the Precedent is a decodeN and its input (a Load) is used at more than one place,
+        // replace this Precedent (decodeN) with the Load instead.
+        if ((my_mem->Opcode() == Op_DecodeN) && (my_mem->in(1)->outcnt() > 1))  {
+          Node* load_node = my_mem->in(1);
+          set_req(MemBarNode::Precedent, load_node);
+          phase->is_IterGVN()->_worklist.push(my_mem);
+          my_mem = load_node;
+        } else {
           assert(my_mem->unique_out() == this, "sanity");
-        phase->hash_delete(this);
           del_req(Precedent);
           phase->is_IterGVN()->_worklist.push(my_mem); // remove dead node later
           my_mem = NULL;
         }
+      }
       if (my_mem != NULL && my_mem->is_Mem()) {
         const TypeOopPtr* t_oop = my_mem->in(MemNode::Address)->bottom_type()->isa_oopptr();
         // Check for scalar replaced object reference.

hotspot/test/compiler/8005956/PolynomialRoot.java

@@ -0,0 +1,776 @@
+//package com.polytechnik.utils;
+/*
+ * (C) Vladislav Malyshkin 2010
+ * This file is under GPL version 3.
+ *
+ */
+
+/** Polynomial root.
+ *  @version $Id: PolynomialRoot.java,v 1.105 2012/08/18 00:00:05 mal Exp $
+ *  @author Vladislav Malyshkin mal@gromco.com
+ */
+
+/**
+* @test
+* @bug 8005956
+* @summary C2: assert(!def_outside->member(r)) failed: Use of external LRG overlaps the same LRG defined in this block
+*
+* @run main PolynomialRoot
+*/
+
+public class PolynomialRoot  {
+
+
+public static int findPolynomialRoots(final int n,
+              final double [] p,
+              final double [] re_root,
+              final double [] im_root)
+{
+    if(n==4)
+    {
+  return root4(p,re_root,im_root);
+    }
+    else if(n==3)
+    {
+  return root3(p,re_root,im_root);
+    }
+    else if(n==2)
+    {
+  return root2(p,re_root,im_root);
+    }
+    else if(n==1)
+    {
+  return root1(p,re_root,im_root);
+    }
+    else
+    {
+  throw new RuntimeException("n="+n+" is not supported yet");
+    }
+}
+
+
+
+static final double SQRT3=Math.sqrt(3.0),SQRT2=Math.sqrt(2.0);
+
+
+private static final boolean PRINT_DEBUG=false;
+
+public static int root4(final double [] p,final double [] re_root,final double [] im_root)
+{
+  if(PRINT_DEBUG) System.err.println("=====================root4:p="+java.util.Arrays.toString(p));
+  final double vs=p[4];
+  if(PRINT_DEBUG) System.err.println("p[4]="+p[4]);
+  if(!(Math.abs(vs)>EPS))
+  {
+      re_root[0]=re_root[1]=re_root[2]=re_root[3]=
+    im_root[0]=im_root[1]=im_root[2]=im_root[3]=Double.NaN;
+      return -1;
+  }
+
+/* zsolve_quartic.c - finds the complex roots of
+ *  x^4 + a x^3 + b x^2 + c x + d = 0
+ */
+  final double a=p[3]/vs,b=p[2]/vs,c=p[1]/vs,d=p[0]/vs;
+  if(PRINT_DEBUG) System.err.println("input a="+a+" b="+b+" c="+c+" d="+d);
+
+
+  final double r4 = 1.0 / 4.0;
+  final double q2 = 1.0 / 2.0, q4 = 1.0 / 4.0, q8 = 1.0 / 8.0;
+  final double q1 = 3.0 / 8.0, q3 = 3.0 / 16.0;
+  final int mt;
+
+  /* Deal easily with the cases where the quartic is degenerate. The
+   * ordering of solutions is done explicitly. */
+  if (0 == b && 0 == c)
+  {
+      if (0 == d)
+      {
+    re_root[0]=-a;
+    im_root[0]=im_root[1]=im_root[2]=im_root[3]=0;
+    re_root[1]=re_root[2]=re_root[3]=0;
+    return 4;
+      }
+      else if (0 == a)
+      {
+    if (d > 0)
+    {
+        final double sq4 = Math.sqrt(Math.sqrt(d));
+        re_root[0]=sq4*SQRT2/2;
+        im_root[0]=re_root[0];
+        re_root[1]=-re_root[0];
+        im_root[1]=re_root[0];
+        re_root[2]=-re_root[0];
+        im_root[2]=-re_root[0];
+        re_root[3]=re_root[0];
+        im_root[3]=-re_root[0];
+        if(PRINT_DEBUG) System.err.println("Path a=0 d>0");
+    }
+    else
+    {
+        final double sq4 = Math.sqrt(Math.sqrt(-d));
+        re_root[0]=sq4;
+        im_root[0]=0;
+        re_root[1]=0;
+        im_root[1]=sq4;
+        re_root[2]=0;
+        im_root[2]=-sq4;
+        re_root[3]=-sq4;
+        im_root[3]=0;
+        if(PRINT_DEBUG) System.err.println("Path a=0 d<0");
+    }
+    return 4;
+      }
+  }
+
+  if (0.0 == c && 0.0 == d)
+  {
+      root2(new double []{p[2],p[3],p[4]},re_root,im_root);
+      re_root[2]=im_root[2]=re_root[3]=im_root[3]=0;
+      return 4;
+  }
+
+  if(PRINT_DEBUG) System.err.println("G Path c="+c+" d="+d);
+  final double [] u=new double[3];
+
+  if(PRINT_DEBUG) System.err.println("Generic Path");
+  /* For non-degenerate solutions, proceed by constructing and
+   * solving the resolvent cubic */
+  final double aa = a * a;
+  final double pp = b - q1 * aa;
+  final double qq = c - q2 * a * (b - q4 * aa);
+  final double rr = d - q4 * a * (c - q4 * a * (b - q3 * aa));
+  final double rc = q2 * pp , rc3 = rc / 3;
+  final double sc = q4 * (q4 * pp * pp - rr);
+  final double tc = -(q8 * qq * q8 * qq);
+  if(PRINT_DEBUG) System.err.println("aa="+aa+" pp="+pp+" qq="+qq+" rr="+rr+" rc="+rc+" sc="+sc+" tc="+tc);
+  final boolean flag_realroots;
+
+  /* This code solves the resolvent cubic in a convenient fashion
+   * for this implementation of the quartic. If there are three real
+   * roots, then they are placed directly into u[].  If two are
+   * complex, then the real root is put into u[0] and the real
+   * and imaginary part of the complex roots are placed into
+   * u[1] and u[2], respectively. */
+  {
+      final double qcub = (rc * rc - 3 * sc);
+      final double rcub = (rc*(2 * rc * rc - 9 * sc) + 27 * tc);
+
+      final double Q = qcub / 9;
+      final double R = rcub / 54;
+
+      final double Q3 = Q * Q * Q;
+      final double R2 = R * R;
+
+      final double CR2 = 729 * rcub * rcub;
+      final double CQ3 = 2916 * qcub * qcub * qcub;
+
+      if(PRINT_DEBUG) System.err.println("CR2="+CR2+" CQ3="+CQ3+" R="+R+" Q="+Q);
+
+      if (0 == R && 0 == Q)
+      {
+    flag_realroots=true;
+    u[0] = -rc3;
+    u[1] = -rc3;
+    u[2] = -rc3;
+      }
+      else if (CR2 == CQ3)
+      {
+    flag_realroots=true;
+    final double sqrtQ = Math.sqrt (Q);
+    if (R > 0)
+    {
+        u[0] = -2 * sqrtQ - rc3;
+        u[1] = sqrtQ - rc3;
+        u[2] = sqrtQ - rc3;
+    }
+    else
+    {
+        u[0] = -sqrtQ - rc3;
+        u[1] = -sqrtQ - rc3;
+        u[2] = 2 * sqrtQ - rc3;
+    }
+      }
+      else if (R2 < Q3)
+      {
+    flag_realroots=true;
+    final double ratio = (R >= 0?1:-1) * Math.sqrt (R2 / Q3);
+    final double theta = Math.acos (ratio);
+    final double norm = -2 * Math.sqrt (Q);
+
+    u[0] = norm * Math.cos (theta / 3) - rc3;
+    u[1] = norm * Math.cos ((theta + 2.0 * Math.PI) / 3) - rc3;
+    u[2] = norm * Math.cos ((theta - 2.0 * Math.PI) / 3) - rc3;
+      }
+      else
+      {
+    flag_realroots=false;
+    final double A = -(R >= 0?1:-1)*Math.pow(Math.abs(R)+Math.sqrt(R2-Q3),1.0/3.0);
+    final double B = Q / A;
+
+    u[0] = A + B - rc3;
+    u[1] = -0.5 * (A + B) - rc3;
+    u[2] = -(SQRT3*0.5) * Math.abs (A - B);
+      }
+      if(PRINT_DEBUG) System.err.println("u[0]="+u[0]+" u[1]="+u[1]+" u[2]="+u[2]+" qq="+qq+" disc="+((CR2 - CQ3) / 2125764.0));
+  }
+  /* End of solution to resolvent cubic */
+
+  /* Combine the square roots of the roots of the cubic
+   * resolvent appropriately. Also, calculate 'mt' which
+   * designates the nature of the roots:
+   * mt=1 : 4 real roots
+   * mt=2 : 0 real roots
+   * mt=3 : 2 real roots
+   */
+
+
+  final double w1_re,w1_im,w2_re,w2_im,w3_re,w3_im,mod_w1w2,mod_w1w2_squared;
+  if (flag_realroots)
+  {
+      mod_w1w2=-1;
+      mt = 2;
+      int jmin=0;
+      double vmin=Math.abs(u[jmin]);
+      for(int j=1;j<3;j++)
+      {
+    final double vx=Math.abs(u[j]);
+    if(vx<vmin)
+    {
+        vmin=vx;
+        jmin=j;
+    }
+      }
+      final double u1=u[(jmin+1)%3],u2=u[(jmin+2)%3];
+      mod_w1w2_squared=Math.abs(u1*u2);
+      if(u1>=0)
+      {
+    w1_re=Math.sqrt(u1);
+    w1_im=0;
+      }
+      else
+      {
+    w1_re=0;
+    w1_im=Math.sqrt(-u1);
+      }
+      if(u2>=0)
+      {
+    w2_re=Math.sqrt(u2);
+    w2_im=0;
+      }
+      else
+      {
+    w2_re=0;
+    w2_im=Math.sqrt(-u2);
+      }
+      if(PRINT_DEBUG) System.err.println("u1="+u1+" u2="+u2+" jmin="+jmin);
+  }
+  else
+  {
+      mt = 3;
+      final double w_mod2_sq=u[1]*u[1]+u[2]*u[2],w_mod2=Math.sqrt(w_mod2_sq),w_mod=Math.sqrt(w_mod2);
+      if(w_mod2_sq<=0)
+      {
+    w1_re=w1_im=0;
+      }
+      else
+      {
+    // calculate square root of a complex number (u[1],u[2])
+    // the result is in the (w1_re,w1_im)
+    final double absu1=Math.abs(u[1]),absu2=Math.abs(u[2]),w;
+    if(absu1>=absu2)
+    {
+        final double t=absu2/absu1;
+        w=Math.sqrt(absu1*0.5 * (1.0 + Math.sqrt(1.0 + t * t)));
+        if(PRINT_DEBUG) System.err.println(" Path1 ");
+    }
+    else
+    {
+        final double t=absu1/absu2;
+        w=Math.sqrt(absu2*0.5 * (t + Math.sqrt(1.0 + t * t)));
+        if(PRINT_DEBUG) System.err.println(" Path1a ");
+    }
+    if(u[1]>=0)
+    {
+        w1_re=w;
+        w1_im=u[2]/(2*w);
+        if(PRINT_DEBUG) System.err.println(" Path2 ");
+    }
+    else
+    {
+        final double vi = (u[2] >= 0) ? w : -w;
+        w1_re=u[2]/(2*vi);
+        w1_im=vi;
+        if(PRINT_DEBUG) System.err.println(" Path2a ");
+    }
+      }
+      final double absu0=Math.abs(u[0]);
+      if(w_mod2>=absu0)
+      {
+    mod_w1w2=w_mod2;
+    mod_w1w2_squared=w_mod2_sq;
+    w2_re=w1_re;
+    w2_im=-w1_im;
+      }
+      else
+      {
+    mod_w1w2=-1;
+    mod_w1w2_squared=w_mod2*absu0;
+    if(u[0]>=0)
+    {
+        w2_re=Math.sqrt(absu0);
+        w2_im=0;
+    }
+    else
+    {
+        w2_re=0;
+        w2_im=Math.sqrt(absu0);
+    }
+      }
+      if(PRINT_DEBUG) System.err.println("u[0]="+u[0]+"u[1]="+u[1]+" u[2]="+u[2]+" absu0="+absu0+" w_mod="+w_mod+" w_mod2="+w_mod2);
+  }
+
+  /* Solve the quadratic in order to obtain the roots
+   * to the quartic */
+  if(mod_w1w2>0)
+  {
+      // a shorcut to reduce rounding error
+      w3_re=qq/(-8)/mod_w1w2;
+      w3_im=0;
+  }
+  else if(mod_w1w2_squared>0)
+  {
+      // regular path
+      final double mqq8n=qq/(-8)/mod_w1w2_squared;
+      w3_re=mqq8n*(w1_re*w2_re-w1_im*w2_im);
+      w3_im=-mqq8n*(w1_re*w2_im+w2_re*w1_im);
+  }
+  else
+  {
+      // typically occur when qq==0
+      w3_re=w3_im=0;
+  }
+
+  final double h = r4 * a;
+  if(PRINT_DEBUG) System.err.println("w1_re="+w1_re+" w1_im="+w1_im+" w2_re="+w2_re+" w2_im="+w2_im+" w3_re="+w3_re+" w3_im="+w3_im+" h="+h);
+
+  re_root[0]=w1_re+w2_re+w3_re-h;
+  im_root[0]=w1_im+w2_im+w3_im;
+  re_root[1]=-(w1_re+w2_re)+w3_re-h;
+  im_root[1]=-(w1_im+w2_im)+w3_im;
+  re_root[2]=w2_re-w1_re-w3_re-h;
+  im_root[2]=w2_im-w1_im-w3_im;
+  re_root[3]=w1_re-w2_re-w3_re-h;
+  im_root[3]=w1_im-w2_im-w3_im;
+
+  return 4;
+}
+
+
+
+    static void setRandomP(final double [] p,final int n,java.util.Random r)
+    {
+  if(r.nextDouble()<0.1)
+  {
+      // integer coefficiens
+      for(int j=0;j<p.length;j++)
+      {
+    if(j<=n)
+    {
+        p[j]=(r.nextInt(2)<=0?-1:1)*r.nextInt(10);
+    }
+    else
+    {
+        p[j]=0;
+    }
+      }
+  }
+  else
+  {
+      // real coefficiens
+      for(int j=0;j<p.length;j++)
+      {
+    if(j<=n)
+    {
+        p[j]=-1+2*r.nextDouble();
+    }
+    else
+    {
+        p[j]=0;
+    }
+      }
+  }
+  if(Math.abs(p[n])<1e-2)
+  {
+      p[n]=(r.nextInt(2)<=0?-1:1)*(0.1+r.nextDouble());
+  }
+    }
+
+
+    static void checkValues(final double [] p,
+          final int n,
+          final double rex,
+          final double imx,
+          final double eps,
+          final String txt)
+    {
+  double res=0,ims=0,sabs=0;
+  final double xabs=Math.abs(rex)+Math.abs(imx);
+  for(int k=n;k>=0;k--)
+  {
+      final double res1=(res*rex-ims*imx)+p[k];
+      final double ims1=(ims*rex+res*imx);
+      res=res1;
+      ims=ims1;
+      sabs+=xabs*sabs+p[k];
+  }
+  sabs=Math.abs(sabs);
+  if(false && sabs>1/eps?
+     (!(Math.abs(res/sabs)<=eps)||!(Math.abs(ims/sabs)<=eps))
+     :
+     (!(Math.abs(res)<=eps)||!(Math.abs(ims)<=eps)))
+  {
+      throw new RuntimeException(
+    getPolinomTXT(p)+"\n"+
+    "\t x.r="+rex+" x.i="+imx+"\n"+
+    "res/sabs="+(res/sabs)+" ims/sabs="+(ims/sabs)+
+    " sabs="+sabs+
+    "\nres="+res+" ims="+ims+" n="+n+" eps="+eps+" "+
+    " sabs>1/eps="+(sabs>1/eps)+
+    " f1="+(!(Math.abs(res/sabs)<=eps)||!(Math.abs(ims/sabs)<=eps))+
+    " f2="+(!(Math.abs(res)<=eps)||!(Math.abs(ims)<=eps))+
+    " "+txt);
+  }
+    }
+
+    static String getPolinomTXT(final double [] p)
+    {
+  final StringBuilder buf=new StringBuilder();
+  buf.append("order="+(p.length-1)+"\t");
+  for(int k=0;k<p.length;k++)
+  {
+      buf.append("p["+k+"]="+p[k]+";");
+  }
+  return buf.toString();
+    }
+
+    static String getRootsTXT(int nr,final double [] re,final double [] im)
+    {
+  final StringBuilder buf=new StringBuilder();
+  for(int k=0;k<nr;k++)
+  {
+      buf.append("x."+k+"("+re[k]+","+im[k]+")\n");
+  }
+  return buf.toString();
+    }
+
+    static void testRoots(final int n,
+        final int n_tests,
+        final java.util.Random rn,
+        final double eps)
+    {
+  final double [] p=new double [n+1];
+  final double [] rex=new double [n],imx=new double [n];
+  for(int i=0;i<n_tests;i++)
+  {
+    for(int dg=n;dg-->-1;)
+    {
+      for(int dr=3;dr-->0;)
+      {
+        setRandomP(p,n,rn);
+        for(int j=0;j<=dg;j++)
+        {
+      p[j]=0;
+        }
+        if(dr==0)
+        {
+      p[0]=-1+2.0*rn.nextDouble();
+        }
+        else if(dr==1)
+        {
+      p[0]=p[1]=0;
+        }
+
+        findPolynomialRoots(n,p,rex,imx);
+
+        for(int j=0;j<n;j++)
+        {
+      //System.err.println("j="+j);
+      checkValues(p,n,rex[j],imx[j],eps," t="+i);
+        }
+      }
+    }
+  }
+  System.err.println("testRoots(): n_tests="+n_tests+" OK, dim="+n);
+    }
+
+
+
+
+    static final double EPS=0;
+
+    public static int root1(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  if(!(Math.abs(p[1])>EPS))
+  {
+      re_root[0]=im_root[0]=Double.NaN;
+      return -1;
+  }
+  re_root[0]=-p[0]/p[1];
+  im_root[0]=0;
+  return 1;
+    }
+
+    public static int root2(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  if(!(Math.abs(p[2])>EPS))
+  {
+      re_root[0]=re_root[1]=im_root[0]=im_root[1]=Double.NaN;
+      return -1;
+  }
+  final double b2=0.5*(p[1]/p[2]),c=p[0]/p[2],d=b2*b2-c;
+  if(d>=0)
+  {
+      final double sq=Math.sqrt(d);
+      if(b2<0)
+      {
+    re_root[1]=-b2+sq;
+    re_root[0]=c/re_root[1];
+      }
+      else if(b2>0)
+      {
+    re_root[0]=-b2-sq;
+    re_root[1]=c/re_root[0];
+      }
+      else
+      {
+    re_root[0]=-b2-sq;
+    re_root[1]=-b2+sq;
+      }
+      im_root[0]=im_root[1]=0;
+  }
+  else
+  {
+      final double sq=Math.sqrt(-d);
+      re_root[0]=re_root[1]=-b2;
+      im_root[0]=sq;
+      im_root[1]=-sq;
+  }
+  return 2;
+    }
+
+    public static int root3(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  final double vs=p[3];
+  if(!(Math.abs(vs)>EPS))
+  {
+      re_root[0]=re_root[1]=re_root[2]=
+    im_root[0]=im_root[1]=im_root[2]=Double.NaN;
+      return -1;
+  }
+  final double a=p[2]/vs,b=p[1]/vs,c=p[0]/vs;
+  /* zsolve_cubic.c - finds the complex roots of x^3 + a x^2 + b x + c = 0
+   */
+  final double q = (a * a - 3 * b);
+  final double r = (a*(2 * a * a - 9 * b) + 27 * c);
+
+  final double Q = q / 9;
+  final double R = r / 54;
+
+  final double Q3 = Q * Q * Q;
+  final double R2 = R * R;
+
+  final double CR2 = 729 * r * r;
+  final double CQ3 = 2916 * q * q * q;
+  final double a3=a/3;
+
+  if (R == 0 && Q == 0)
+  {
+      re_root[0]=re_root[1]=re_root[2]=-a3;
+      im_root[0]=im_root[1]=im_root[2]=0;
+      return 3;
+  }
+  else if (CR2 == CQ3)
+  {
+      /* this test is actually R2 == Q3, written in a form suitable
+         for exact computation with integers */
+
+      /* Due to finite precision some double roots may be missed, and
+         will be considered to be a pair of complex roots z = x +/-
+         epsilon i close to the real axis. */
+
+      final double sqrtQ = Math.sqrt (Q);
+
+      if (R > 0)
+      {
+    re_root[0] = -2 * sqrtQ - a3;
+    re_root[1]=re_root[2]=sqrtQ - a3;
+    im_root[0]=im_root[1]=im_root[2]=0;
+      }
+      else
+      {
+    re_root[0]=re_root[1] = -sqrtQ - a3;
+    re_root[2]=2 * sqrtQ - a3;
+    im_root[0]=im_root[1]=im_root[2]=0;
+      }
+      return 3;
+  }
+  else if (R2 < Q3)
+  {
+      final double sgnR = (R >= 0 ? 1 : -1);
+      final double ratio = sgnR * Math.sqrt (R2 / Q3);
+      final double theta = Math.acos (ratio);
+      final double norm = -2 * Math.sqrt (Q);
+      final double r0 = norm * Math.cos (theta/3) - a3;
+      final double r1 = norm * Math.cos ((theta + 2.0 * Math.PI) / 3) - a3;
+      final double r2 = norm * Math.cos ((theta - 2.0 * Math.PI) / 3) - a3;
+
+      re_root[0]=r0;
+      re_root[1]=r1;
+      re_root[2]=r2;
+      im_root[0]=im_root[1]=im_root[2]=0;
+      return 3;
+  }
+  else
+  {
+      final double sgnR = (R >= 0 ? 1 : -1);
+      final double A = -sgnR * Math.pow (Math.abs (R) + Math.sqrt (R2 - Q3), 1.0 / 3.0);
+      final double B = Q / A;
+
+      re_root[0]=A + B - a3;
+      im_root[0]=0;
+      re_root[1]=-0.5 * (A + B) - a3;
+      im_root[1]=-(SQRT3*0.5) * Math.abs(A - B);
+      re_root[2]=re_root[1];
+      im_root[2]=-im_root[1];
+      return 3;
+  }
+
+    }
+
+
+    static void root3a(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  if(Math.abs(p[3])>EPS)
+  {
+      final double v=p[3],
+    a=p[2]/v,b=p[1]/v,c=p[0]/v,
+    a3=a/3,a3a=a3*a,
+    pd3=(b-a3a)/3,
+    qd2=a3*(a3a/3-0.5*b)+0.5*c,
+    Q=pd3*pd3*pd3+qd2*qd2;
+      if(Q<0)
+      {
+    // three real roots
+    final double SQ=Math.sqrt(-Q);
+    final double th=Math.atan2(SQ,-qd2);
+    im_root[0]=im_root[1]=im_root[2]=0;
+    final double f=2*Math.sqrt(-pd3);
+    re_root[0]=f*Math.cos(th/3)-a3;
+    re_root[1]=f*Math.cos((th+2*Math.PI)/3)-a3;
+    re_root[2]=f*Math.cos((th+4*Math.PI)/3)-a3;
+    //System.err.println("3r");
+      }
+      else
+      {
+    // one real & two complex roots
+    final double SQ=Math.sqrt(Q);
+    final double r1=-qd2+SQ,r2=-qd2-SQ;
+    final double v1=Math.signum(r1)*Math.pow(Math.abs(r1),1.0/3),
+        v2=Math.signum(r2)*Math.pow(Math.abs(r2),1.0/3),
+        sv=v1+v2;
+    // real root
+    re_root[0]=sv-a3;
+    im_root[0]=0;
+    // complex roots
+    re_root[1]=re_root[2]=-0.5*sv-a3;
+    im_root[1]=(v1-v2)*(SQRT3*0.5);
+    im_root[2]=-im_root[1];
+    //System.err.println("1r2c");
+      }
+  }
+  else
+  {
+      re_root[0]=re_root[1]=re_root[2]=im_root[0]=im_root[1]=im_root[2]=Double.NaN;
+  }
+    }
+
+
+    static void printSpecialValues()
+    {
+  for(int st=0;st<6;st++)
+  {
+      //final double [] p=new double []{8,1,3,3.6,1};
+      final double [] re_root=new double [4],im_root=new double [4];
+      final double [] p;
+      final int n;
+      if(st<=3)
+      {
+    if(st<=0)
+    {
+        p=new double []{2,-4,6,-4,1};
+        //p=new double []{-6,6,-6,8,-2};
+    }
+    else if(st==1)
+    {
+        p=new double []{0,-4,8,3,-9};
+    }
+    else if(st==2)
+    {
+        p=new double []{-1,0,2,0,-1};
+    }
+    else
+    {
+        p=new double []{-5,2,8,-2,-3};
+    }
+    root4(p,re_root,im_root);
+    n=4;
+      }
+      else
+      {
+    p=new double []{0,2,0,1};
+    if(st==4)
+    {
+        p[1]=-p[1];
+    }
+    root3(p,re_root,im_root);
+    n=3;
+      }
+      System.err.println("======== n="+n);
+      for(int i=0;i<=n;i++)
+      {
+    if(i<n)
+    {
+        System.err.println(String.valueOf(i)+"\t"+
+               p[i]+"\t"+
+               re_root[i]+"\t"+
+               im_root[i]);
+    }
+    else
+    {
+        System.err.println(String.valueOf(i)+"\t"+p[i]+"\t");
+    }
+      }
+  }
+    }
+
+
+
+    public static void main(final String [] args)
+    {
+  final long t0=System.currentTimeMillis();
+  final double eps=1e-6;
+  //checkRoots();
+  final java.util.Random r=new java.util.Random(-1381923);
+  printSpecialValues();
+
+  final int n_tests=10000000;
+  //testRoots(2,n_tests,r,eps);
+  //testRoots(3,n_tests,r,eps);
+  testRoots(4,n_tests,r,eps);
+  final long t1=System.currentTimeMillis();
+  System.err.println("PolynomialRoot.main: "+n_tests+" tests OK done in "+(t1-t0)+" milliseconds. ver=$Id: PolynomialRoot.java,v 1.105 2012/08/18 00:00:05 mal Exp $");
+    }
+
+
+
+}