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This commit is contained in:
Vladimir Kozlov 2013-06-27 11:12:19 -07:00
commit 579c7ac5ab
11 changed files with 800 additions and 363 deletions
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8
hotspot/make/linux/makefiles/gcc.make
View file

@ -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

6
hotspot/src/cpu/sparc/vm/macroAssembler_sparc.cpp
View file

@ -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;

30
hotspot/src/cpu/sparc/vm/relocInfo_sparc.cpp
View file

@ -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) {
}

24
hotspot/src/cpu/x86/vm/relocInfo_x86.cpp
View file

@ -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()) {

16
hotspot/src/cpu/zero/vm/relocInfo_zero.cpp
View file

@ -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();

5
hotspot/src/share/vm/code/nmethod.cpp
View file

@ -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");
}
}

145
hotspot/src/share/vm/code/relocInfo.cpp
View file

@ -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

126
hotspot/src/share/vm/code/relocInfo.hpp
View file

@ -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 = 13, // metadata that used to be oops
metadata_type = 12, // 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

9
hotspot/src/share/vm/interpreter/bytecodeInterpreter.cpp
View file

@ -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();
VERIFY_OOP(method);
if (VerifyOops) method->verify();
if (cache->has_appendix()) {
ConstantPool* constants = METHOD->constants();

10
hotspot/src/share/vm/opto/memnode.cpp
View file

@ -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.

776
hotspot/test/compiler/8005956/PolynomialRoot.java Normal file
View file

@ -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 $");
}
}