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Author SHA1 Message Date
henrit
e50c7a6de8 ECMA compliant Math object.
git-svn-id: svn://10.0.0.236/branches/jsmath_henrit@3974 18797224-902f-48f8-a5cc-f745e15eee43
1998-06-17 14:56:25 +00:00
henrit
0e59d9a6a0 ECMA compliant Math object
git-svn-id: svn://10.0.0.236/branches/jsmath_henrit@3972 18797224-902f-48f8-a5cc-f745e15eee43
1998-06-17 14:47:15 +00:00
henrit
ed2ac58da0 ECMA compliant Math object
git-svn-id: svn://10.0.0.236/branches/jsmath_henrit@3970 18797224-902f-48f8-a5cc-f745e15eee43
1998-06-17 14:40:48 +00:00
henrit
a9328119cb ECMA compliant Math object
git-svn-id: svn://10.0.0.236/branches/jsmath_henrit@3969 18797224-902f-48f8-a5cc-f745e15eee43
1998-06-17 14:29:21 +00:00
henrit
16be25fcbf ECMA compliant Math object.
git-svn-id: svn://10.0.0.236/branches/jsmath_henrit@3968 18797224-902f-48f8-a5cc-f745e15eee43
1998-06-17 14:06:16 +00:00
(no author)
b4d0709d23 This commit was manufactured by cvs2svn to create branch 'jsmath_henrit'.
git-svn-id: svn://10.0.0.236/branches/jsmath_henrit@3951 18797224-902f-48f8-a5cc-f745e15eee43
1998-06-16 23:10:58 +00:00
347 changed files with 123969 additions and 5146 deletions

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@@ -1,134 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#include "Fundamentals.h"
#include "BitSet.h"
// Return the next bit after index set to true or -1 if none.
//
Int32 BitSet::nextOne(Int32 pos) const
{
++pos;
if (pos < 0 || Uint32(pos) >= universeSize)
return -1;
Uint32 offset = getWordOffset(pos);
Uint8 index = getBitOffset(pos);
Word* ptr = &word[offset];
Word currentWord = *ptr++ >> index;
if (currentWord != Word(0)) {
while ((currentWord & Word(1)) == 0) {
++index;
currentWord >>= 1;
}
return (offset << nBitsInWordLog2) + index;
}
Word* limit = &word[getSizeInWords(universeSize)];
while (ptr < limit) {
++offset;
currentWord = *ptr++;
if (currentWord != Word(0)) {
index = 0;
while ((currentWord & Word(1)) == 0) {
++index;
currentWord >>= 1;
}
return (offset << nBitsInWordLog2) + index;
}
}
return -1;
}
// Return the next bit after index set to false or -1 if none.
//
Int32 BitSet::nextZero(Int32 pos) const
{
++pos;
if (pos < 0 || Uint32(pos) >= universeSize)
return -1;
Uint32 offset = getWordOffset(pos);
Uint8 index = getBitOffset(pos);
Word* ptr = &word[offset];
Word currentWord = *ptr++ >> index;
if (currentWord != Word(~0)) {
for (; index < nBitsInWord; ++index) {
if ((currentWord & Word(1)) == 0) {
Int32 ret = (offset << nBitsInWordLog2) + index;
return (Uint32(ret) < universeSize) ? ret : -1;
}
currentWord >>= 1;
}
}
Word* limit = &word[getSizeInWords(universeSize)];
while (ptr < limit) {
++offset;
currentWord = *ptr++;
if (currentWord != Word(~0)) {
for (index = 0; index < nBitsInWord; ++index) {
if ((currentWord & Word(1)) == 0) {
Int32 ret = (offset << nBitsInWordLog2) + index;
return (Uint32(ret) < universeSize) ? ret : -1;
}
currentWord >>= 1;
}
}
}
return -1;
}
#ifdef DEBUG_LOG
// Print the set.
//
void BitSet::printPretty(LogModuleObject log)
{
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("[ "));
for (Int32 i = firstOne(); i != -1; i = nextOne(i)) {
Int32 currentBit = i;
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("%d", currentBit));
Int32 nextBit = nextOne(currentBit);
if (nextBit != currentBit + 1) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, (" "));
continue;
}
while ((nextBit != -1) && (nextBit == (currentBit + 1))) {
currentBit = nextBit;
nextBit = nextOne(nextBit);
}
if (currentBit > (i+1))
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("-%d ", currentBit));
else
UT_OBJECTLOG(log, PR_LOG_ALWAYS, (" %d ", currentBit));
i = currentBit;
}
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("]\n"));
}
#endif // DEBUG_LOG

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@@ -1,195 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _BITSET_H_
#define _BITSET_H_
#include "Fundamentals.h"
#include "LogModule.h"
#include "Pool.h"
#include <string.h>
//------------------------------------------------------------------------------
// BitSet -
class BitSet
{
private:
#if (PR_BITS_PER_WORD == 64)
typedef Uint64 Word;
#elif (PR_BITS_PER_WORD == 32)
typedef Uint32 Word;
#endif
static const nBitsInWord = PR_BITS_PER_WORD;
static const nBytesInWord = PR_BYTES_PER_WORD;
static const nBitsInWordLog2 = PR_BITS_PER_WORD_LOG2;
static const nBytesInWordLog2 = PR_BYTES_PER_WORD_LOG2;
// Return the number of Word need to store the universe.
static Uint32 getSizeInWords(Uint32 sizeOfUniverse) {return (sizeOfUniverse + (nBitsInWord - 1)) >> nBitsInWordLog2;}
// Return the given element offset in its containing Word.
static Uint32 getBitOffset(Uint32 element) {return element & (nBitsInWord - 1);}
// Return the Word offset for the given element int the universe.
static Uint32 getWordOffset(Uint32 element) {return element >> nBitsInWordLog2;}
// Return the mask for the given bit index.
static Word getMask(Uint8 index) {return Word(1) << index;}
private:
Uint32 universeSize; // Size of the universe
Word* word; // universe memory.
private:
// No copy constructor.
BitSet(const BitSet&);
// Check if the given set's universe is of the same size than this universe.
void checkUniverseCompatibility(const BitSet& set) const {assert(set.universeSize == universeSize);}
// Check if pos is valid for this set's universe.
void checkMember(Int32 pos) const {assert(pos >=0 && Uint32(pos) < universeSize);}
public:
// Create a bitset of universeSize bits.
BitSet(Pool& pool, Uint32 universeSize) : universeSize(universeSize) {word = new(pool) Word[getSizeInWords(universeSize)]; clear();}
// Return the size of this bitset.
Uint32 getSize() const {return universeSize;}
// Clear the bitset.
void clear() {memset(word, 0x00, getSizeInWords(universeSize) << nBytesInWordLog2);}
// Clear the bit at index.
void clear(Uint32 index) {checkMember(index); word[getWordOffset(index)] &= ~getMask(index);}
// Set the bitset.
void set() {memset(word, 0xFF, getSizeInWords(universeSize) << nBytesInWordLog2);}
// Set the bit at index.
void set(Uint32 index) {checkMember(index); word[getWordOffset(index)] |= getMask(index);}
// Return true if the bit at index is set.
bool test(Uint32 index) const {checkMember(index); return (word[getWordOffset(index)] & getMask(index)) != 0;}
// Union with the given bitset.
inline void or(const BitSet& set);
// Intersection with the given bitset.
inline void and(const BitSet& set);
// Difference with the given bitset.
inline void difference(const BitSet& set);
// Copy set.
inline BitSet& operator = (const BitSet& set);
// Return true if the bitset are identical.
friend bool operator == (const BitSet& set1, const BitSet& set2);
// Return true if the bitset are different.
friend bool operator != (const BitSet& set1, const BitSet& set2);
// Logical operators.
BitSet& operator |= (const BitSet& set) {or(set); return *this;}
BitSet& operator &= (const BitSet& set) {and(set); return *this;}
BitSet& operator -= (const BitSet& set) {difference(set); return *this;}
// Return the first bit at set to true or -1 if none.
Int32 firstOne() const {return nextOne(-1);}
// Return the next bit after index set to true or -1 if none.
Int32 nextOne(Int32 pos) const;
// Return the first bit at set to false or -1 if none.
Int32 firstZero() const {return nextZero(-1);}
// Return the next bit after index set to false or -1 if none.
Int32 nextZero(Int32 pos) const;
// Iterator to conform with the set API.
typedef Int32 iterator;
// Return true if the walk is ordered.
static bool isOrdered() {return true;}
// Return the iterator for the first element of this set.
iterator begin() const {return firstOne();}
// Return the next iterator.
iterator advance(iterator pos) const {return nextOne(pos);}
// Return true if the iterator is at the end of the set.
bool done(iterator pos) const {return pos == -1;}
// Return the element corresponding to the given iterator.
Uint32 get(iterator pos) const {return pos;}
#ifdef DEBUG_LOG
// Print the set.
void printPretty(LogModuleObject log);
#endif // DEBUG_LOG
};
// Union with the given bitset.
//
inline void BitSet::or(const BitSet& set)
{
checkUniverseCompatibility(set);
Word* src = set.word;
Word* dst = word;
Word* limit = &src[getSizeInWords(universeSize)];
while (src < limit)
*dst++ |= *src++;
}
// Intersection with the given bitset.
//
inline void BitSet::and(const BitSet& set)
{
checkUniverseCompatibility(set);
Word* src = set.word;
Word* dst = word;
Word* limit = &src[getSizeInWords(universeSize)];
while (src < limit)
*dst++ &= *src++;
}
// Difference with the given bitset.
//
inline void BitSet::difference(const BitSet& set)
{
checkUniverseCompatibility(set);
Word* src = set.word;
Word* dst = word;
Word* limit = &src[getSizeInWords(universeSize)];
while (src < limit)
*dst++ &= ~*src++;
}
// Copy the given set into this set.
//
inline BitSet& BitSet::operator = (const BitSet& set)
{
checkUniverseCompatibility(set);
if (this != &set)
memcpy(word, set.word, getSizeInWords(universeSize) << nBytesInWordLog2);
return *this;
}
// Return true if the given set is identical to this set.
inline bool operator == (const BitSet& set1, const BitSet& set2)
{
set1.checkUniverseCompatibility(set2);
if (&set1 == &set2)
return true;
return memcmp(set1.word, set2.word, BitSet::getSizeInWords(set1.universeSize) << BitSet::nBytesInWordLog2) == 0;
}
inline bool operator != (const BitSet& set1, const BitSet& set2) {return !(set1 == set2);}
#endif // _BITSET_H

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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _COALESCING_H_
#define _COALESCING_H_
#include "Fundamentals.h"
#include "Pool.h"
#include "RegisterPressure.h"
#include "InterferenceGraph.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Instruction.h"
#include "SparseSet.h"
#include "RegisterAllocator.h"
#include "RegisterAllocatorTools.h"
#if 1
// Performing an ultra conservative coalescing meens that when we look at
// candidates (source,destination) for coalescing we need to make sure
// that the combined interference of the source and destination register
// will not exceed the total number of register available for the register
// class.
#define ULTRA_CONSERVATIVE_COALESCING
#else
// If we are not doing an ultra conservative coalescing we have to make sure
// that the total number of neighbor whose degree is greater than the total
// number of register is not greater than the total number of register.
#undef ULTRA_CONSERVATIVE_COALESCING
#endif
template <class RegisterPressure>
struct Coalescing
{
static bool coalesce(RegisterAllocator& registerAllocator);
};
template <class RegisterPressure>
bool Coalescing<RegisterPressure>::coalesce(RegisterAllocator& registerAllocator)
{
Pool& pool = registerAllocator.pool;
// Initialize the lookup table
//
Uint32 rangeCount = registerAllocator.rangeCount;
RegisterName* newRange = new RegisterName[2 * rangeCount];
RegisterName* coalescedRange = &newRange[rangeCount];
RegisterName* name2range = registerAllocator.name2range;
init(coalescedRange, rangeCount);
SparseSet interferences(pool, rangeCount);
InterferenceGraph<RegisterPressure>& iGraph = registerAllocator.iGraph;
bool removedInstructions = false;
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.lndList;
Uint32 nNodes = controlGraph.nNodes;
// Walk the nodes in the loop nesting depth list.
for (Int32 n = nNodes - 1; n >= 0; n--) {
InstructionList& instructions = nodes[n]->getInstructions();
InstructionList::iterator it = instructions.begin();
while (!instructions.done(it)) {
Instruction& instruction = instructions.get(it);
it = instructions.advance(it);
if ((instruction.getFlags() & ifCopy) != 0) {
assert(instruction.getInstructionUseBegin() != instruction.getInstructionUseEnd() && instruction.getInstructionUseBegin()[0].isRegister());
assert(instruction.getInstructionDefineBegin() != instruction.getInstructionDefineEnd() && instruction.getInstructionDefineBegin()[0].isRegister());
RegisterName source = findRoot(name2range[instruction.getInstructionUseBegin()[0].getRegisterName()], coalescedRange);
RegisterName destination = findRoot(name2range[instruction.getInstructionDefineBegin()[0].getRegisterName()], coalescedRange);
if (source == destination) {
instruction.remove();
} else if (!iGraph.interfere(source, destination)) {
InterferenceVector* sourceVector = iGraph.getInterferenceVector(source);
InterferenceVector* destinationVector = iGraph.getInterferenceVector(destination);
#ifdef ULTRA_CONSERVATIVE_COALESCING
interferences.clear();
InterferenceVector* vector;
for (vector = sourceVector; vector != NULL; vector = vector->next) {
RegisterName* neighbors = vector->neighbors;
for (Uint32 i = 0; i < vector->count; i++)
interferences.set(findRoot(neighbors[i], coalescedRange));
}
for (vector = destinationVector; vector != NULL; vector = vector->next) {
RegisterName* neighbors = vector->neighbors;
for (Uint32 i = 0; i < vector->count; i++)
interferences.set(findRoot(neighbors[i], coalescedRange));
}
Uint32 count = interferences.getSize();
#else // ULTRA_CONSERVATIVE_COALESCING
trespass("not implemented");
Uint32 count = 0;
#endif // ULTRA_CONSERVATIVE_COALESCING
if (count < 6 /* FIX: should get the number from the class */) {
// Update the interferences vector.
if (sourceVector == NULL) {
iGraph.setInterferenceVector(source, destinationVector);
sourceVector = destinationVector;
} else if (destinationVector == NULL)
iGraph.setInterferenceVector(destination, sourceVector);
else {
InterferenceVector* last = NULL;
for (InterferenceVector* v = sourceVector; v != NULL; v = v->next)
last = v;
assert(last);
last->next = destinationVector;
iGraph.setInterferenceVector(destination, sourceVector);
}
// Update the interference matrix.
for (InterferenceVector* v = sourceVector; v != NULL; v = v->next) {
RegisterName* neighbors = v->neighbors;
for (Uint32 i = 0; i < v->count; i++) {
RegisterName neighbor = findRoot(neighbors[i], coalescedRange);
iGraph.setInterference(neighbor, source);
iGraph.setInterference(neighbor, destination);
}
}
instruction.remove();
coalescedRange[source] = destination;
removedInstructions = true;
}
}
}
}
}
registerAllocator.rangeCount = compress(registerAllocator.name2range, coalescedRange, registerAllocator.nameCount, rangeCount);
delete newRange;
return removedInstructions;
}
#endif // _COALESCING_H_

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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef NEW_LAURENTM_CODE
#include "Coloring.h"
#include "VirtualRegister.h"
#include "FastBitSet.h"
#include "FastBitMatrix.h"
#include "CpuInfo.h"
bool Coloring::
assignRegisters(FastBitMatrix& interferenceMatrix)
{
PRUint32 *stackPtr = new(pool) PRUint32[vRegManager.count()];
return select(interferenceMatrix, stackPtr, simplify(interferenceMatrix, stackPtr));
}
PRInt32 Coloring::
getLowestSpillCostRegister(FastBitSet& bitset)
{
PRInt32 lowest = bitset.firstOne();
if (lowest != -1)
{
Flt32 cost = vRegManager.getVirtualRegister(lowest).spillInfo.spillCost;
for (PRInt32 r = bitset.nextOne(lowest); r != -1; r = bitset.nextOne(r))
{
VirtualRegister& vReg = vRegManager.getVirtualRegister(r);
if (!vReg.spillInfo.infiniteSpillCost && (vReg.spillInfo.spillCost < cost))
{
cost = vReg.spillInfo.spillCost;
lowest = r;
}
}
}
return lowest;
}
PRUint32* Coloring::
simplify(FastBitMatrix interferenceMatrix, PRUint32* stackPtr)
{
// first we construct the sets low and high. low contains all nodes of degree
// inferior to the number of register available on the processor. All the
// nodes with an high degree and a finite spill cost are placed in high.
// Nodes of high degree and infinite spill cost are not included in either sets.
PRUint32 nRegisters = vRegManager.count();
FastBitSet low(pool, nRegisters);
FastBitSet high(pool, nRegisters);
FastBitSet stack(pool, nRegisters);
for (VirtualRegisterManager::iterator i = vRegManager.begin(); !vRegManager.done(i); i = vRegManager.advance(i))
{
VirtualRegister& vReg = vRegManager.getVirtualRegister(i);
if (vReg.getClass() == vrcStackSlot)
{
stack.set(i);
vReg.colorRegister(nRegisters);
}
else
{
if (vReg.colorInfo.interferenceDegree < NUMBER_OF_REGISTERS)
low.set(i);
else // if (!vReg.spillInfo.infiniteSpillCost)
high.set(i);
// Set coloring info.
vReg.spillInfo.willSpill = false;
switch(vReg.getClass())
{
case vrcInteger:
vReg.colorRegister(LAST_GREGISTER + 1);
break;
case vrcFloatingPoint:
case vrcFixedPoint:
vReg.colorRegister(LAST_FPREGISTER + 1);
break;
default:
PR_ASSERT(false); // Cannot happen.
}
}
}
// push the stack registers
PRInt32 j;
for (j = stack.firstOne(); j != -1; j = stack.nextOne(j))
*stackPtr++ = j;
// simplify
while (true)
{
PRInt32 r;
while ((r = getLowestSpillCostRegister(low)) != -1)
{
VirtualRegister& vReg = vRegManager.getVirtualRegister(r);
/* update low and high */
FastBitSet inter(interferenceMatrix.getRow(r), nRegisters);
for (j = inter.firstOne(); j != -1; j = inter.nextOne(j))
{
VirtualRegister& neighbor = vRegManager.getVirtualRegister(j);
// if the new interference degree of one of his neighbor becomes
// NUMBER_OF_REGISTERS - 1 then it is added to the set 'low'.
PRUint32 maxInterference = 0;
switch (neighbor.getClass())
{
case vrcInteger:
maxInterference = NUMBER_OF_GREGISTERS;
break;
case vrcFloatingPoint:
case vrcFixedPoint:
maxInterference = NUMBER_OF_FPREGISTERS;
break;
default:
PR_ASSERT(false);
}
if ((vRegManager.getVirtualRegister(j).colorInfo.interferenceDegree-- == maxInterference))
{
high.clear(j);
low.set(j);
}
vReg.colorInfo.interferenceDegree--;
interferenceMatrix.clear(r, j);
interferenceMatrix.clear(j, r);
}
low.clear(r);
// Push this register.
*stackPtr++ = r;
}
if ((r = getLowestSpillCostRegister(high)) != -1)
{
high.clear(r);
low.set(r);
}
else
break;
}
return stackPtr;
}
bool Coloring::
select(FastBitMatrix& interferenceMatrix, PRUint32* stackBase, PRUint32* stackPtr)
{
PRUint32 nRegisters = vRegManager.count();
FastBitSet usedRegisters(NUMBER_OF_REGISTERS + 1); // usedRegisters if used for both GR & FPR.
FastBitSet preColoredRegisters(NUMBER_OF_REGISTERS + 1);
FastBitSet usedStack(nRegisters + 1);
bool success = true;
Int32 lastUsedSSR = -1;
// select
while (stackPtr != stackBase)
{
// Pop one register.
PRUint32 r = *--stackPtr;
VirtualRegister& vReg = vRegManager.getVirtualRegister(r);
FastBitSet neighbors(interferenceMatrix.getRow(r), nRegisters);
if (vReg.getClass() == vrcStackSlot)
// Stack slots coloring.
{
usedStack.clear();
for (PRInt32 i = neighbors.firstOne(); i != -1; i = neighbors.nextOne(i))
usedStack.set(vRegManager.getVirtualRegister(i).getColor());
Int32 color = usedStack.firstZero();
vReg.colorRegister(color);
if (color > lastUsedSSR)
lastUsedSSR = color;
}
else
// Integer & Floating point register coloring.
{
usedRegisters.clear();
preColoredRegisters.clear();
for (PRInt32 i = neighbors.firstOne(); i != -1; i = neighbors.nextOne(i))
{
VirtualRegister& nvReg = vRegManager.getVirtualRegister(i);
usedRegisters.set(nvReg.getColor());
if (nvReg.isPreColored())
preColoredRegisters.set(nvReg.getPreColor());
}
if (vReg.hasSpecialInterference)
usedRegisters |= vReg.specialInterference;
PRInt8 c = -1;
PRInt8 maxColor = 0;
PRInt8 firstColor = 0;
switch (vReg.getClass())
{
case vrcInteger:
firstColor = FIRST_GREGISTER;
maxColor = LAST_GREGISTER;
break;
case vrcFloatingPoint:
case vrcFixedPoint:
firstColor = FIRST_FPREGISTER;
maxColor = LAST_FPREGISTER;
break;
default:
PR_ASSERT(false);
}
if (vReg.isPreColored())
{
c = vReg.getPreColor();
if (usedRegisters.test(c))
c = -1;
}
else
{
for (c = usedRegisters.nextZero(firstColor - 1); (c >= 0) && (c <= maxColor) && (preColoredRegisters.test(c));
c = usedRegisters.nextZero(c)) {}
}
if ((c >= 0) && (c <= maxColor))
{
vReg.colorRegister(c);
}
else
{
VirtualRegister& stackRegister = vRegManager.newVirtualRegister(vrcStackSlot);
vReg.equivalentRegister[vrcStackSlot] = &stackRegister;
vReg.spillInfo.willSpill = true;
success = false;
}
}
}
#ifdef DEBUG
if (success)
{
for (VirtualRegisterManager::iterator i = vRegManager.begin(); !vRegManager.done(i); i = vRegManager.advance(i))
{
VirtualRegister& vReg = vRegManager.getVirtualRegister(i);
switch (vReg.getClass())
{
case vrcInteger:
if (vReg.getColor() > LAST_GREGISTER)
PR_ASSERT(false);
break;
case vrcFloatingPoint:
case vrcFixedPoint:
#if NUMBER_OF_FPREGISTERS != 0
if (vReg.getColor() > LAST_FPREGISTER)
PR_ASSERT(false);
#endif
break;
default:
break;
}
}
}
#endif
vRegManager.nUsedStackSlots = lastUsedSSR + 1;
return success;
}
#endif // NEW_LAURENTM_CODE

View File

@@ -1,284 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#include "Fundamentals.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Instruction.h"
#include "RegisterAllocator.h"
#include "VirtualRegister.h"
#include "InterferenceGraph.h"
#include "SparseSet.h"
#include "Spilling.h"
#include "Splits.h"
UT_EXTERN_LOG_MODULE(RegAlloc);
template <class RegisterPressure>
class Coloring
{
private:
static RegisterName* simplify(RegisterAllocator& registerAllocator, RegisterName* coloringStack);
static bool select(RegisterAllocator& registerAllocator, RegisterName* coloringStack, RegisterName* coloringStackPtr);
public:
static bool color(RegisterAllocator& registerAllocator);
static void finalColoring(RegisterAllocator& registerAllocator);
};
template <class RegisterPressure>
void Coloring<RegisterPressure>::finalColoring(RegisterAllocator& registerAllocator)
{
RegisterName* color = registerAllocator.color;
RegisterName* name2range = registerAllocator.name2range;
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
for (Uint32 n = 0; n < nNodes; n++) {
InstructionList& instructions = nodes[n]->getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
usePtr->setRegisterName(color[name2range[usePtr->getRegisterName()]]);
#ifdef DEBUG
RegisterID rid = usePtr->getRegisterID();
setColoredRegister(rid);
usePtr->setRegisterID(rid);
#endif // DEBUG
}
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
definePtr->setRegisterName(color[name2range[definePtr->getRegisterName()]]);
#ifdef DEBUG
RegisterID rid = definePtr->getRegisterID();
setColoredRegister(rid);
definePtr->setRegisterID(rid);
#endif // DEBUG
}
}
}
}
template <class RegisterPressure>
bool Coloring<RegisterPressure>::select(RegisterAllocator& registerAllocator, RegisterName* coloringStack, RegisterName* coloringStackPtr)
{
Uint32 rangeCount = registerAllocator.rangeCount;
RegisterName* color = new RegisterName[rangeCount];
registerAllocator.color = color;
for (Uint32 r = 1; r < rangeCount; r++)
color[r] = RegisterName(6); // FIX;
// Color the preColored registers.
//
VirtualRegisterManager& vrManager = registerAllocator.vrManager;
RegisterName* name2range = registerAllocator.name2range;
PreColoredRegister* machineEnd = vrManager.getMachineRegistersEnd();
for (PreColoredRegister* machinePtr = vrManager.getMachineRegistersBegin(); machinePtr < machineEnd; machinePtr++)
if (machinePtr->id != invalidID) {
color[name2range[getName(machinePtr->id)]] = machinePtr->color;
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\twill preColor range %d as %d\n", name2range[getName(machinePtr->id)], machinePtr->color));
}
SpillCost* cost = registerAllocator.spillCost;
Pool& pool = registerAllocator.pool;
SparseSet& spill = *new(pool) SparseSet(pool, rangeCount);
registerAllocator.willSpill = &spill;
SparseSet neighborColors(pool, 6); // FIX
InterferenceGraph<RegisterPressure>& iGraph = registerAllocator.iGraph;
bool coloringFailed = false;
while (coloringStackPtr > coloringStack) {
RegisterName range = *--coloringStackPtr;
if (!cost[range].infinite && cost[range].cost < 0) {
coloringFailed = true;
spill.set(range);
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\tfailed to color %d, will spill.\n", range));
} else {
neighborColors.clear();
for (InterferenceVector* vector = iGraph.getInterferenceVector(range); vector != NULL; vector = vector->next)
for (Int32 i = vector->count - 1; i >= 0; --i) {
RegisterName neighborColor = color[vector->neighbors[i]];
if (neighborColor < 6) // FIX
neighborColors.set(neighborColor);
}
if (neighborColors.getSize() == 6) { // FIX
coloringFailed = true;
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\tfailed to color %d, ", range));
if (!Splits<RegisterPressure>::findSplit(registerAllocator, color, range)) {
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("will spill.\n"));
spill.set(range);
} else
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("will split.\n"));
} else {
for (Uint32 i = 0; i < 6; i++) // FIX
if (!neighborColors.test(i)) {
fprintf(stdout, "\twill color %d as %d\n", range, i);
color[range] = RegisterName(i);
break;
}
}
}
}
#ifdef DEBUG_LOG
if (coloringFailed) {
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("Coloring failed:\n"));
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\twill spill: "));
spill.printPretty(UT_LOG_MODULE(RegAlloc));
} else {
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("Coloring succeeded:\n"));
for (Uint32 i = 1; i < rangeCount; i++)
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\trange %d colored as %d\n", i, color[i]));
}
#endif
return !coloringFailed;
}
template <class RegisterPressure>
RegisterName* Coloring<RegisterPressure>::simplify(RegisterAllocator& registerAllocator, RegisterName* coloringStack)
{
InterferenceGraph<RegisterPressure>& iGraph = registerAllocator.iGraph;
SpillCost* spillCost = registerAllocator.spillCost;
Uint32 rangeCount = registerAllocator.rangeCount;
Uint32* degree = new Uint32[rangeCount];
for (RegisterName i = RegisterName(1); i < rangeCount; i = RegisterName(i + 1)) {
InterferenceVector* vector = iGraph.getInterferenceVector(i);
degree[i] = (vector != NULL) ? vector->count : 0;
}
Pool& pool = registerAllocator.pool;
SparseSet low(pool, rangeCount);
SparseSet high(pool, rangeCount);
SparseSet highInfinite(pool, rangeCount);
SparseSet preColored(pool, rangeCount);
// Get the precolored registers.
//
VirtualRegisterManager& vrManager = registerAllocator.vrManager;
RegisterName* name2range = registerAllocator.name2range;
PreColoredRegister* machineEnd = vrManager.getMachineRegistersEnd();
for (PreColoredRegister* machinePtr = vrManager.getMachineRegistersBegin(); machinePtr < machineEnd; machinePtr++)
if (machinePtr->id != invalidID)
preColored.set(name2range[getName(machinePtr->id)]);
// Insert the live ranges in the sets.
//
for (Uint32 range = 1; range < rangeCount; range++)
if (!preColored.test(range))
if (degree[range] < 6) // FIX
low.set(range);
else if (!spillCost[range].infinite)
high.set(range);
else
highInfinite.set(range);
#ifdef DEBUG_LOG
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("Coloring sets:\n\tlow = "));
low.printPretty(UT_LOG_MODULE(RegAlloc));
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\thigh = "));
high.printPretty(UT_LOG_MODULE(RegAlloc));
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\thighInfinite = "));
highInfinite.printPretty(UT_LOG_MODULE(RegAlloc));
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\tpreColored = "));
preColored.printPretty(UT_LOG_MODULE(RegAlloc));
#endif // DEBUG_LOG
RegisterName* coloringStackPtr = coloringStack;
while (low.getSize() != 0 || high.getSize() != 0) {
while (low.getSize() != 0) {
RegisterName range = RegisterName(low.getOne());
low.clear(range);
*coloringStackPtr++ = range;
for (InterferenceVector* vector = iGraph.getInterferenceVector(range); vector != NULL; vector = vector->next)
for (Int32 i = (vector->count - 1); i >= 0; --i) {
RegisterName neighbor = vector->neighbors[i];
degree[neighbor]--;
if (degree[neighbor] < 6) // FIX
if (high.test(neighbor)) {
high.clear(neighbor);
low.set(neighbor);
} else if (highInfinite.test(neighbor)) {
highInfinite.clear(neighbor);
low.set(neighbor);
}
}
}
if (high.getSize() != 0) {
RegisterName best = RegisterName(high.getOne());
double bestCost = spillCost[best].cost;
double bestDegree = degree[best];
// Choose the next best candidate.
//
for (SparseSet::iterator i = high.begin(); !high.done(i); i = high.advance(i)) {
RegisterName range = RegisterName(high.get(i));
double thisCost = spillCost[range].cost;
double thisDegree = degree[range];
if (thisCost * bestDegree < bestCost * thisDegree) {
best = range;
bestCost = thisCost;
bestDegree = thisDegree;
}
}
high.clear(best);
low.set(best);
}
}
assert(highInfinite.getSize() == 0);
delete degree;
#ifdef DEBUG_LOG
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("Coloring stack:\n\t"));
for (RegisterName* sp = coloringStack; sp < coloringStackPtr; ++sp)
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("%d ", *sp));
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\n"));
#endif // DEBUG_LOG
return coloringStackPtr;
}
template <class RegisterPressure>
bool Coloring<RegisterPressure>::color(RegisterAllocator& registerAllocator)
{
RegisterName* coloringStack = new RegisterName[registerAllocator.rangeCount];
return select(registerAllocator, coloringStack, simplify(registerAllocator, coloringStack));
}

View File

@@ -1,212 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#include "Fundamentals.h"
#include <string.h>
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "DominatorGraph.h"
DominatorGraph::DominatorGraph(ControlGraph& controlGraph) : controlGraph(controlGraph)
{
Uint32 nNodes = controlGraph.nNodes;
GtoV = new Uint32[nNodes + 1];
VtoG = new Uint32[nNodes + 1];
Uint32 v = 1;
for (Uint32 n = 0; n < nNodes; n++) {
VtoG[v] = n;
GtoV[n] = v++;
}
// Initialize all the 1-based arrays.
//
parent = new Uint32[v];
semi = new Uint32[v];
vertex = new Uint32[v];
label = new Uint32[v];
size = new Uint32[v];
ancestor = new Uint32[v];
child = new Uint32[v];
dom = new Uint32[v];
bucket = new DGLinkedList*[v];
memset(semi, '\0', v * sizeof(Uint32));
memset(bucket, '\0', v * sizeof(DGLinkedList*));
vCount = v;
build();
delete parent;
delete semi;
delete vertex;
delete label;
delete size;
delete ancestor;
delete child;
delete dom;
delete bucket;
}
Uint32 DominatorGraph::DFS(Uint32 vx, Uint32 n)
{
semi[vx] = ++n;
vertex[n] = label[vx] = vx;
ancestor[vx] = child[vx] = 0;
size[vx] = 1;
ControlNode& node = *controlGraph.dfsList[VtoG[vx]];
ControlEdge* successorEnd = node.getSuccessorsEnd();
for (ControlEdge* successorPtr = node.getSuccessorsBegin(); successorPtr < successorEnd; successorPtr++) {
Uint32 w = GtoV[successorPtr->getTarget().dfsNum];
if (semi[w] == 0) {
parent[w] = vx;
n = DFS(w, n);
}
}
return n;
}
void DominatorGraph::LINK(Uint32 vx, Uint32 w)
{
Uint32 s = w;
while (semi[label[w]] < semi[label[child[s]]]) {
if (size[s] + size[child[child[s]]] >= (size[child[s]] << 1)) {
ancestor[child[s]] = s;
child[s] = child[child[s]];
} else {
size[child[s]] = size[s];
s = ancestor[s] = child[s];
}
}
label[s] = label[w];
size[vx] += size[w];
if(size[vx] < (size[w] << 1)) {
Uint32 t = s;
s = child[vx];
child[vx] = t;
}
while( s != 0 ) {
ancestor[s] = vx;
s = child[s];
}
}
void DominatorGraph::COMPRESS(Uint32 vx)
{
if(ancestor[ancestor[vx]] != 0) {
COMPRESS(ancestor[vx]);
if(semi[label[ancestor[vx]]] < semi[label[vx]])
label[vx] = label[ancestor[vx]];
ancestor[vx] = ancestor[ancestor[vx]];
}
}
Uint32 DominatorGraph::EVAL(Uint32 vx)
{
if(ancestor[vx] == 0)
return label[vx];
COMPRESS(vx);
return (semi[label[ancestor[vx]]] >= semi[label[vx]]) ? label[vx] : label[ancestor[vx]];
}
void DominatorGraph::build()
{
Uint32 n = DFS(GtoV[0], 0);
size[0] = label[0] = semi[0];
for (Uint32 i = n; i >= 2; i--) {
Uint32 w = vertex[i];
ControlNode& node = *controlGraph.dfsList[VtoG[w]];
const DoublyLinkedList<ControlEdge>& predecessors = node.getPredecessors();
for (DoublyLinkedList<ControlEdge>::iterator p = predecessors.begin(); !predecessors.done(p); p = predecessors.advance(p)) {
Uint32 vx = GtoV[predecessors.get(p).getSource().dfsNum];
Uint32 u = EVAL(vx);
if(semi[u] < semi[w])
semi[w] = semi[u];
}
DGLinkedList* elem = new DGLinkedList();
elem->next = bucket[vertex[semi[w]]];
elem->index = w;
bucket[vertex[semi[w]]] = elem;
LINK(parent[w], w);
elem = bucket[parent[w]];
while(elem != NULL) {
Uint32 vx = elem->index;
Uint32 u = EVAL(vx);
dom[vx] = (semi[u] < semi[vx]) ? u : parent[w];
elem = elem->next;
}
}
memset(size, '\0', n * sizeof(Uint32));
Pool& pool = controlGraph.pool;
nodes = new(pool) DGNode[n];
for(Uint32 j = 2; j <= n; j++) {
Uint32 w = vertex[j];
Uint32 d = dom[w];
if(d != vertex[semi[w]]) {
d = dom[d];
dom[w] = d;
}
size[d]++;
}
dom[GtoV[0]] = 0;
for (Uint32 k = 1; k <= n; k++) {
DGNode& node = nodes[VtoG[k]];
Uint32 count = size[k];
node.successorsEnd = node.successorsBegin = (count) ? new(pool) Uint32[count] : (Uint32*) 0;
}
for (Uint32 l = 2; l <= n; l++)
*(nodes[VtoG[dom[l]]].successorsEnd)++ = VtoG[l];
}
#ifdef DEBUG_LOG
void DominatorGraph::printPretty(LogModuleObject log)
{
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("Dominator Graph:\n"));
Uint32 nNodes = controlGraph.nNodes;
for (Uint32 i = 0; i < nNodes; i++) {
DGNode& node = nodes[i];
if (node.successorsBegin != node.successorsEnd) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\tN%d dominates ", i));
for (Uint32* successorsPtr = node.successorsBegin; successorsPtr < node.successorsEnd; successorsPtr++)
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("N%d ", *successorsPtr));
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\n"));
}
}
}
#endif // DEBUG_LOG

View File

@@ -1,80 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _DOMINATOR_GRAPH_H_
#define _DOMINATOR_GRAPH_H_
#include "LogModule.h"
class ControlGraph;
struct DGNode
{
Uint32* successorsBegin;
Uint32* successorsEnd;
};
struct DGLinkedList
{
DGLinkedList* next;
Uint32 index;
};
class DominatorGraph
{
private:
ControlGraph& controlGraph;
Uint32 vCount;
Uint32* VtoG;
Uint32* GtoV;
Uint32* parent;
Uint32* semi;
Uint32* vertex;
Uint32* label;
Uint32* size;
Uint32* ancestor;
Uint32* child;
Uint32* dom;
DGLinkedList** bucket;
DGNode* nodes;
private:
void build();
Uint32 DFS(Uint32 vx, Uint32 n);
void LINK(Uint32 vx, Uint32 w);
void COMPRESS(Uint32 vx);
Uint32 EVAL(Uint32 vx);
public:
DominatorGraph(ControlGraph& controlGraph);
Uint32* getSuccessorsBegin(Uint32 n) const {return nodes[n].successorsBegin;}
Uint32* getSuccessorsEnd(Uint32 n) const {return nodes[n].successorsEnd;}
#ifdef DEBUG_LOG
void printPretty(LogModuleObject log);
#endif // DEBUG_LOG
};
#endif // _DOMINATOR_GRAPH_H_

View File

@@ -1,97 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _HASH_SET_H_
#define _HASH_SET_H_
#include "Fundamentals.h"
#include "Pool.h"
#include <string.h>
struct HashSetElement
{
Uint32 index;
HashSetElement* next;
};
class HashSet
{
private:
static const hashSize = 64;
// Return the hash code for the given element index.
static Uint32 getHashCode(Uint32 index) {return index & (hashSize - 1);} // Could be better !
private:
Pool& allocationPool;
HashSetElement** bucket;
HashSetElement* free;
private:
// No copy constructor.
HashSet(const HashSet&);
// No copy operator.
void operator = (const HashSet&);
public:
// Create a new HashSet.
inline HashSet(Pool& pool, Uint32 universeSize);
// Clear the hashset.
void clear();
// Clear the element for the given index.
void clear(Uint32 index);
// Set the element for the given index.
void set(Uint32 index);
// Return true if the element at index is a member.
bool test(Uint32 index) const;
// Union with the given hashset.
inline void or(const HashSet& set);
// Intersection with the given hashset.
inline void and(const HashSet& set);
// Difference with the given hashset.
inline void difference(const HashSet& set);
// Logical operators.
HashSet& operator |= (const HashSet& set) {or(set); return *this;}
HashSet& operator &= (const HashSet& set) {and(set); return *this;}
HashSet& operator -= (const HashSet& set) {difference(set); return *this;}
// Iterator to conform with the set API.
typedef HashSetElement* iterator;
// Return the iterator for the first element of this set.
iterator begin() const;
// Return the next iterator.
iterator advance(iterator pos) const;
// Return true if the iterator is at the end of the set.
bool done(iterator pos) const {return pos == NULL;}
};
inline HashSet::HashSet(Pool& pool, Uint32 /*universeSize*/)
: allocationPool(pool), free(NULL)
{
bucket = new(pool) HashSetElement*[hashSize];
memset(bucket, '\0', sizeof(HashSetElement*));
}
#endif // _HASH_SET_H_

View File

@@ -1,213 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _INDEXED_POOL_H_
#define _INDEXED_POOL_H_
#include "Fundamentals.h"
#include <string.h>
#include <stdlib.h>
//------------------------------------------------------------------------------
// IndexedPool<IndexedObjectSubclass> is an indexed pool of objects. The
// template parameter 'IndexedObjectSubclass' must be a subclass of the struct
// IndexedObject.
//
// When the indexed pool is ask to allocate and initialize a new object (using
// the operator new(anIndexedPool) it will zero the memory used to store the
// object and initialize the field 'index' of this object to its position in
// the pool.
//
// An object allocated by the indexed pool can be freed by calling the method
// IndexedPool::release(IndexedElement& objectIndex).
//
// example:
//
// IndexedPool<IndexedElement> elementPool;
//
// IndexedElement& element1 = *new(elementPool) IndexedElement();
// IndexedElement& element2 = *new(elementPool) IndexedElement();
//
// indexedPool.release(element1);
// IndexedElement& element3 = *new(elementPool) IndexedElement();
//
// At this point element1 is no longer a valid object, element2 is at
// index 2 and element3 is at index 1.
//
//------------------------------------------------------------------------------
// IndexedObject -
//
template<class Object>
struct IndexedObject
{
Uint32 index; // Index in the pool.
Object* next; // Used to link IndexedObject together.
Uint32 getIndex() {return index;}
};
//------------------------------------------------------------------------------
// IndexedPool<IndexedObject> -
//
template <class IndexedObject>
class IndexedPool
{
private:
static const blockSize = 4; // Size of one block.
Uint32 nBlocks; // Number of blocks in the pool.
IndexedObject** block; // Array of block pointers.
IndexedObject* freeObjects; // Chained list of free IndexedObjects.
Uint32 nextIndex; // Index of the next free object in the last block.
private:
void allocateAnotherBlock();
IndexedObject& newObject();
public:
IndexedPool() : nBlocks(0), block(NULL), freeObjects(NULL), nextIndex(1) {}
~IndexedPool();
IndexedObject& get(Uint32 index) const;
void release(IndexedObject& object);
void setSize(Uint32 size) {assert(size < nextIndex); nextIndex = size;}
// Return the universe size.
Uint32 getSize() {return nextIndex;}
friend void* operator new(size_t, IndexedPool<IndexedObject>& pool); // Needs to call newObject().
};
// Free all the memory allocated for this object.
//
template <class IndexedObject>
IndexedPool<IndexedObject>::~IndexedPool()
{
for (Uint32 n = 0; n < nBlocks; n++)
free(&((IndexedObject **) &block[n][n*blockSize])[-(n + 1)]);
}
// Release the given. This object will be iserted in the chained
// list of free IndexedObjects. To minimize the fragmentation the chained list
// is ordered by ascending indexes.
//
template <class IndexedObject>
void IndexedPool<IndexedObject>::release(IndexedObject& object)
{
Uint32 index = object.index;
IndexedObject* list = freeObjects;
assert(&object == &get(index)); // Make sure that object is owned by this pool.
if (list == NULL) { // The list is empty.
freeObjects = &object;
object.next = NULL;
} else { // The list contains at least 1 element.
if (index < list->index) { // insert as first element.
freeObjects = &object;
object.next = list;
} else { // Find this object's place.
while ((list->next) != NULL && (list->next->index < index))
list = list->next;
object.next = list->next;
list->next = &object;
}
}
#ifdef DEBUG
// Sanity check to be sure that the list is correctly ordered.
for (IndexedObject* obj = freeObjects; obj != NULL; obj = obj->next)
if (obj->next != NULL)
assert(obj->index < obj->next->index);
#endif
}
// Create a new block of IndexedObjects. We will allocate the memory to
// store IndexedPool::blockSize IndexedObject and the new Array of block
// pointers.
// The newly created IndexedObjects will not be initialized.
//
template <class IndexedObject>
void IndexedPool<IndexedObject>::allocateAnotherBlock()
{
void* memory = (void *) malloc((nBlocks + 1) * sizeof(Uint32) + blockSize * sizeof(IndexedObject));
memcpy(memory, block, nBlocks * sizeof(Uint32));
block = (IndexedObject **) memory;
IndexedObject* objects = (IndexedObject *) &block[nBlocks + 1];
block[nBlocks] = &objects[-(nBlocks * blockSize)];
nBlocks++;
}
// Return the IndexedObject at the position 'index' in the pool.
//
template <class IndexedObject>
IndexedObject& IndexedPool<IndexedObject>::get(Uint32 index) const
{
Uint32 blockIndex = index / blockSize;
assert(blockIndex < nBlocks);
return block[blockIndex][index];
}
// Return the reference of an unused object in the pool.
//
template <class IndexedObject>
IndexedObject& IndexedPool<IndexedObject>::newObject()
{
if (freeObjects != NULL) {
IndexedObject& newObject = *freeObjects;
freeObjects = newObject.next;
return newObject;
}
Uint32 nextIndex = this->nextIndex++;
Uint32 blockIndex = nextIndex / blockSize;
while (blockIndex >= nBlocks)
allocateAnotherBlock();
IndexedObject& newObject = block[blockIndex][nextIndex];
newObject.index = nextIndex;
return newObject;
}
// Return the address of the next unsused object in the given
// indexed pool. The field index of the newly allocated object
// will be initialized to the corresponding index of this object
// in the pool.
//
template <class IndexedObject>
void* operator new(size_t size, IndexedPool<IndexedObject>& pool)
{
assert(size == sizeof(IndexedObject));
return (void *) &pool.newObject();
}
#endif // _INDEXED_POOL_H_

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@@ -1,258 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _INTERFERENCE_GRAPH_H_
#define _INTERFERENCE_GRAPH_H_
#include "Fundamentals.h"
#include "ControlGraph.h"
#include "Primitives.h"
#include "Instruction.h"
#include "VirtualRegister.h"
#include "RegisterPressure.h"
#include "SparseSet.h"
#include <string.h>
struct InterferenceVector
{
Uint32 count;
InterferenceVector* next;
RegisterName* neighbors;
InterferenceVector() : count(0), next(NULL) {}
};
class RegisterAllocator;
template <class RegisterPressure>
class InterferenceGraph
{
private:
RegisterAllocator& registerAllocator;
RegisterPressure::Set* interferences;
InterferenceVector** vector;
Uint32* offset;
Uint32 rangeCount;
private:
// No copy constructor.
InterferenceGraph(const InterferenceGraph&);
// No copy operator.
void operator = (const InterferenceGraph&);
// Check if reg is a member of the universe.
void checkMember(RegisterName name) {assert(name < rangeCount);}
// Return the edge index for the interference between name1 and name2.
Uint32 getEdgeIndex(RegisterName name1, RegisterName name2);
public:
InterferenceGraph(RegisterAllocator& registerAllocator) : registerAllocator(registerAllocator) {}
// Calculate the interferences.
void build();
// Return true if reg1 and reg2 interfere.
bool interfere(RegisterName name1, RegisterName name2);
// Return the interference vector for the given register or NULL if there is none.
InterferenceVector* getInterferenceVector(RegisterName name) {return vector[name];}
// Set the interference between name1 and name2.
void setInterference(RegisterName name1, RegisterName name2);
// Set the interference vector for the given register.
void setInterferenceVector(RegisterName name, InterferenceVector* v) {vector[name] = v;}
#ifdef DEBUG_LOG
// Print the interferences.
void printPretty(LogModuleObject log);
#endif // DEBUG_LOG
};
template <class RegisterPressure>
void InterferenceGraph<RegisterPressure>::build()
{
Pool& pool = registerAllocator.pool;
Uint32 rangeCount = registerAllocator.rangeCount;
this->rangeCount = rangeCount;
// Initialize the structures.
//
offset = new(pool) Uint32[rangeCount + 1];
vector = new(pool) InterferenceVector*[rangeCount];
memset(vector, '\0', sizeof(InterferenceVector*) * rangeCount);
Uint32 o = 0;
offset[0] = 0;
for (Uint32 i = 1; i <= rangeCount; ++i) {
offset[i] = o;
o += i;
}
interferences = new(pool) RegisterPressure::Set(pool, (rangeCount * rangeCount) / 2);
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
RegisterName* name2range = registerAllocator.name2range;
LivenessInfo<RegisterPressure> liveness = Liveness<RegisterPressure>::analysis(controlGraph, rangeCount, name2range);
registerAllocator.liveness = liveness;
SparseSet currentLive(pool, rangeCount);
for (Uint32 n = 0; n < nNodes; n++) {
ControlNode& node = *nodes[n];
currentLive = liveness.liveOut[n];
InstructionList& instructions = node.getInstructions();
for (InstructionList::iterator i = instructions.end(); !instructions.done(i); i = instructions.retreat(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useBegin = instruction.getInstructionUseBegin();
InstructionUse* useEnd = instruction.getInstructionUseEnd();
InstructionUse* usePtr;
InstructionDefine* defineBegin = instruction.getInstructionDefineBegin();
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
InstructionDefine* definePtr;
// Handle the copy instruction to avoid unnecessary interference between the 2 registers.
if ((instruction.getFlags() & ifCopy) != 0) {
assert(useBegin != useEnd && useBegin[0].isRegister());
currentLive.clear(name2range[useBegin[0].getRegisterName()]);
}
// Create the interferences.
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
RegisterName define = name2range[definePtr->getRegisterName()];
for (SparseSet::iterator e = currentLive.begin(); !currentLive.done(e); e = currentLive.advance(e)) {
RegisterName live = RegisterName(currentLive.get(e));
if ((live != define) && !interfere(live, define) && registerAllocator.canInterfere(live, define)) {
if (vector[define] == NULL)
vector[define] = new(pool) InterferenceVector();
vector[define]->count++;
if (vector[live] == NULL)
vector[live] = new(pool) InterferenceVector();
vector[live]->count++;
setInterference(live, define);
}
}
}
// Now update the liveness.
//
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
currentLive.clear(name2range[definePtr->getRegisterName()]);
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
currentLive.set(name2range[usePtr->getRegisterName()]);
}
}
// Allocate the memory to store the interferences.
//
for (Uint32 e = 0; e < rangeCount; e++)
if (vector[e] != NULL) {
InterferenceVector& v = *vector[e];
v.neighbors = new(pool) RegisterName[v.count];
v.count = 0;
}
// Initialize the edges.
//
if (RegisterPressure::Set::isOrdered()) {
RegisterName name1 = RegisterName(0);
for (RegisterPressure::Set::iterator i = interferences->begin(); !interferences->done(i); i = interferences->advance(i)) {
Uint32 interferenceIndex = interferences->get(i);
while(interferenceIndex >= offset[name1 + 1])
name1 = RegisterName(name1 + 1);
assert((interferenceIndex >= offset[name1]) && (interferenceIndex < offset[name1 + 1]));
RegisterName name2 = RegisterName(interferenceIndex - offset[name1]);
assert(interfere(name1, name2));
InterferenceVector& vector1 = *vector[name1];
vector1.neighbors[vector1.count++] = name2;
InterferenceVector& vector2 = *vector[name2];
vector2.neighbors[vector2.count++] = name1;
}
} else {
trespass("not Implemented"); // FIX: need one more pass to initialize the vectors.
}
}
template <class RegisterPressure>
Uint32 InterferenceGraph<RegisterPressure>::getEdgeIndex(RegisterName name1, RegisterName name2)
{
checkMember(name1); checkMember(name2);
assert(name1 != name2); // This is not possible.
return (name1 < name2) ? offset[name2] + name1 : offset[name1] + name2;
}
template <class RegisterPressure>
void InterferenceGraph<RegisterPressure>::setInterference(RegisterName name1, RegisterName name2)
{
interferences->set(getEdgeIndex(name1, name2));
}
template <class RegisterPressure>
bool InterferenceGraph<RegisterPressure>::interfere(RegisterName name1, RegisterName name2)
{
return interferences->test(getEdgeIndex(name1, name2));
}
#ifdef DEBUG_LOG
template <class RegisterPressure>
void InterferenceGraph<RegisterPressure>::printPretty(LogModuleObject log)
{
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("Interference Vectors:\n"));
for (Uint32 i = 1; i < rangeCount; i++) {
if (vector[i] != NULL) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\tvr%d: (", i));
for (InterferenceVector* v = vector[i]; v != NULL; v = v->next)
for (Uint32 j = 0; j < v->count; j++) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("%d", v->neighbors[j]));
if (v->next != NULL || j != (v->count - 1))
UT_OBJECTLOG(log, PR_LOG_ALWAYS, (","));
}
UT_OBJECTLOG(log, PR_LOG_ALWAYS, (")\n"));
}
}
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("Interference Matrix:\n"));
for (RegisterName name1 = RegisterName(1); name1 < rangeCount; name1 = RegisterName(name1 + 1)) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\t%d:\t", name1));
for (RegisterName name2 = RegisterName(1); name2 < rangeCount; name2 = RegisterName(name2 + 1))
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("%c", ((name1 != name2) && interfere(name1, name2)) ? '1' : '0'));
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\n"));
}
}
#endif // DEBUG_LOG
#endif // _INTERFERENCE_GRAPH_H_

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@@ -1,87 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _LIVE_RANGE_H_
#define _LIVE_RANGE_H_
#include "Fundamentals.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Primitives.h"
#include "Instruction.h"
#include "RegisterAllocator.h"
#include "RegisterAllocatorTools.h"
template <class RegisterPressure>
struct LiveRange
{
static void build(RegisterAllocator& registerAllocator);
};
template <class RegisterPressure>
void LiveRange<RegisterPressure>::build(RegisterAllocator& registerAllocator)
{
// Intialize the lookup table.
//
Uint32 nameCount = registerAllocator.nameCount;
RegisterName* nameTable = new(registerAllocator.pool) RegisterName[2*nameCount];
RegisterName* rangeName = &nameTable[nameCount];
init(rangeName, nameCount);
// Walk the graph.
//
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
SparseSet destination(registerAllocator.pool, nameCount);
for (Uint32 n = 0; n < nNodes; n++) {
InstructionList& phiNodes = nodes[n]->getPhiNodeInstructions();
destination.clear();
for (InstructionList::iterator i = phiNodes.begin(); !phiNodes.done(i); i = phiNodes.advance(i)) {
Instruction& phiNode = phiNodes.get(i);
assert(phiNode.getInstructionDefineBegin() != phiNode.getInstructionDefineEnd() && phiNode.getInstructionDefineBegin()[0].isRegister());
destination.set(findRoot(phiNode.getInstructionDefineBegin()[0].getRegisterName(), rangeName));
}
for (InstructionList::iterator p = phiNodes.begin(); !phiNodes.done(p); p = phiNodes.advance(p)) {
Instruction& phiNode = phiNodes.get(p);
assert(phiNode.getInstructionDefineBegin() != phiNode.getInstructionDefineEnd() && phiNode.getInstructionDefineBegin()[0].isRegister());
RegisterName destinationName = phiNode.getInstructionDefineBegin()[0].getRegisterName();
RegisterName destinationRoot = findRoot(destinationName, rangeName);
InstructionUse* useEnd = phiNode.getInstructionUseEnd();
for (InstructionUse* usePtr = phiNode.getInstructionUseBegin(); usePtr < useEnd; usePtr++) {
assert(usePtr->isRegister());
RegisterName sourceName = usePtr->getRegisterName();
RegisterName sourceRoot = findRoot(sourceName, rangeName);
if (sourceRoot != destinationRoot && !destination.test(sourceRoot))
rangeName[sourceRoot] = destinationRoot;
}
}
}
registerAllocator.rangeCount = compress(registerAllocator.name2range, rangeName, nameCount, nameCount);
}
#endif // _LIVE_RANGE_H_

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@@ -1,163 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _LIVE_RANGE_GRAPH_
#define _LIVE_RANGE_GRAPH_
#include "Fundamentals.h"
#include "Pool.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Instruction.h"
#include "RegisterTypes.h"
class RegisterAllocator;
template <class RegisterPressure>
class LiveRangeGraph
{
private:
RegisterAllocator& registerAllocator;
RegisterPressure::Set* edges;
Uint32 rangeCount;
public:
//
//
LiveRangeGraph(RegisterAllocator& registerAllocator) : registerAllocator(registerAllocator) {}
//
//
void build();
//
//
void addEdge(RegisterName name1, RegisterName name2);
//
//
bool haveEdge(RegisterName name1, RegisterName name2);
#ifdef DEBUG_LOG
//
//
void printPretty(LogModuleObject log);
#endif // DEBUG_LOG
};
template <class RegisterPressure>
void LiveRangeGraph<RegisterPressure>::build()
{
Pool& pool = registerAllocator.pool;
Uint32 rangeCount = registerAllocator.rangeCount;
this->rangeCount = rangeCount;
edges = new(pool) RegisterPressure::Set(pool, rangeCount * rangeCount);
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
RegisterName* name2range = registerAllocator.name2range;
LivenessInfo<RegisterPressure>& liveness = registerAllocator.liveness;
SparseSet currentLive(pool, rangeCount);
for (Uint32 n = 0; n < nNodes; n++) {
ControlNode& node = *nodes[n];
currentLive = liveness.liveOut[n];
InstructionList& instructions = node.getInstructions();
for (InstructionList::iterator i = instructions.end(); !instructions.done(i); i = instructions.retreat(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useBegin = instruction.getInstructionUseBegin();
InstructionUse* useEnd = instruction.getInstructionUseEnd();
InstructionUse* usePtr;
InstructionDefine* defineBegin = instruction.getInstructionDefineBegin();
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
InstructionDefine* definePtr;
if ((instruction.getFlags() & ifCopy) != 0) {
assert(useBegin != useEnd && useBegin[0].isRegister());
currentLive.clear(name2range[useBegin[0].getRegisterName()]);
}
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
RegisterName define = name2range[definePtr->getRegisterName()];
for (SparseSet::iterator l = currentLive.begin(); !currentLive.done(l); l = currentLive.advance(l)) {
RegisterName live = RegisterName(currentLive.get(l));
if (define != live && registerAllocator.canInterfere(define, live))
addEdge(define, live);
}
}
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
currentLive.clear(name2range[definePtr->getRegisterName()]);
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
currentLive.set(name2range[usePtr->getRegisterName()]);
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName use = name2range[usePtr->getRegisterName()];
for (SparseSet::iterator l = currentLive.begin(); !currentLive.done(l); l = currentLive.advance(l)) {
RegisterName live = RegisterName(currentLive.get(l));
if (use != live && registerAllocator.canInterfere(use, live))
addEdge(use, live);
}
}
}
}
}
template <class RegisterPressure>
void LiveRangeGraph<RegisterPressure>::addEdge(RegisterName name1, RegisterName name2)
{
assert(name1 != name2);
edges->set(name1 * rangeCount + name2);
}
template <class RegisterPressure>
bool LiveRangeGraph<RegisterPressure>::haveEdge(RegisterName name1, RegisterName name2)
{
assert(name1 != name2);
return edges->test(name1 * rangeCount + name2);
}
#ifdef DEBUG_LOG
template <class RegisterPressure>
void LiveRangeGraph<RegisterPressure>::printPretty(LogModuleObject log)
{
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("Live ranges graph:\n"));
for (RegisterName name1 = RegisterName(1); name1 < rangeCount; name1 = RegisterName(name1 + 1)) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\t%d:\t", name1));
for (RegisterName name2 = RegisterName(1); name2 < rangeCount; name2 = RegisterName(name2 + 1))
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("%c", ((name1 != name2) && haveEdge(name1, name2)) ? '1' : '0'));
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\n"));
}
}
#endif // DEBUG_LOG
#endif // _LIVE_RANGE_GRAPH_

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@@ -1,301 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _LIVENESS_H_
#define _LIVENESS_H_
#include "Fundamentals.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Instruction.h"
#include "RegisterTypes.h"
// ----------------------------------------------------------------------------
// LivenessInfo -
template <class RegisterPressure>
struct LivenessInfo
{
RegisterPressure::Set* liveIn;
RegisterPressure::Set* liveOut;
DEBUG_LOG_ONLY(Uint32 size);
#ifdef DEBUG_LOG
void printPretty(LogModuleObject log);
#endif // DEBUG_LOG
};
// ----------------------------------------------------------------------------
// Liveness
//
// The liveness is defined by the following data-flow equations:
//
// LiveIn(n) = LocalLive(n) U (LiveOut(n) - Killed(n)).
// LiveOut(n) = U LiveIn(s) (s a successor of n).
//
// where LocalLive(n) is the set of used registers in the block n, Killed(n)
// is the set of defined registers in the block n, LiveIn(n) is the set of
// live registers at the begining of the block n and LiveOut(n) is the set
// of live registers at the end of the block n.
//
//
// We will compute the liveness analysis in two stages:
//
// 1- Build LocalLive(n) (wich is an approximation of LiveIn(n)) and Killed(n)
// for each block n.
// 2- Perform a backward data-flow analysis to propagate the liveness information
// through the entire control-flow graph.
//
template <class RegisterPressure>
struct Liveness
{
static LivenessInfo<RegisterPressure> analysis(ControlGraph& controlGraph, Uint32 rangeCount, const RegisterName* name2range);
static LivenessInfo<RegisterPressure> analysis(ControlGraph& controlGraph, Uint32 nameCount);
};
template <class RegisterPressure>
LivenessInfo<RegisterPressure> Liveness<RegisterPressure>::analysis(ControlGraph& controlGraph, Uint32 rangeCount, const RegisterName* name2range)
{
Pool& pool = controlGraph.pool;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
// Allocate the temporary sets.
RegisterPressure::Set* killed = new(pool) RegisterPressure::Set[nNodes](pool, rangeCount);
// Allocate the globals sets.
RegisterPressure::Set* liveIn = new(pool) RegisterPressure::Set[nNodes](pool, rangeCount);
RegisterPressure::Set* liveOut = new(pool) RegisterPressure::Set[nNodes](pool, rangeCount);
// First stage of the liveness analysis: Compute the sets LocalLive(stored in LiveIn) and Killed.
//
for (Uint32 n = 0; n < (nNodes - 1); n++) {
ControlNode& node = *nodes[n];
RegisterPressure::Set& currentLocalLive = liveIn[n];
RegisterPressure::Set& currentKilled = killed[n];
// Find the instructions contributions to the sets LocalLive and Killed.
//
InstructionList& instructions = node.getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
Instruction& instruction = instructions.get(i);
// If a VirtualRegister is 'used' before being 'defined' then we add it to set LocalLive.
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
Uint32 index = name2range[usePtr->getRegisterName()];
if (!currentKilled.test(index))
currentLocalLive.set(index);
}
// If a Virtualregister is 'defined' then we add it to the set Killed.
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
currentKilled.set(name2range[definePtr->getRegisterName()]);
}
}
// Second stage of the liveness analysis: We propagate the LiveIn & LiveOut through the entire
// control-flow graph.
//
RegisterPressure::Set temp(pool, rangeCount);
bool changed;
do {
changed = false;
// For all nodes is this graph except the endNode.
for (Int32 n = (nNodes - 2); n >= 0; n--) {
ControlNode& node = *nodes[n];
RegisterPressure::Set& currentLiveIn = liveIn[n];
RegisterPressure::Set& currentLiveOut = liveOut[n];
// Compute temp = Union of LiveIn(s) (s a successor of this node) | usedByPhiNodes(n).
// temp will be the new LiveOut(n).
Uint32 nSuccessors = node.nSuccessors();
if (nSuccessors != 0) {
temp = liveIn[node.nthSuccessor(0).getTarget().dfsNum];
for (Uint32 s = 1; s < nSuccessors; s++)
temp |= liveIn[node.nthSuccessor(s).getTarget().dfsNum];
} else
temp.clear();
// If temp and LiveOut(n) differ then set LiveOut(n) = temp and recalculate the
// new LiveIn(n).
if (currentLiveOut != temp) {
currentLiveOut = temp;
temp -= killed[n]; // FIX: could be optimized with one call to unionDiff !
temp |= currentLiveIn;
if (currentLiveIn != temp) {
currentLiveIn = temp;
changed = true;
}
}
}
} while(changed);
LivenessInfo<RegisterPressure> liveness;
liveness.liveIn = liveIn;
liveness.liveOut = liveOut;
DEBUG_LOG_ONLY(liveness.size = nNodes);
return liveness;
}
template <class RegisterPressure>
LivenessInfo<RegisterPressure> Liveness<RegisterPressure>::analysis(ControlGraph& controlGraph, Uint32 nameCount)
{
Pool& pool = controlGraph.pool;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
// Allocate the temporary sets.
RegisterPressure::Set* killed = new(pool) RegisterPressure::Set[nNodes](pool, nameCount);
RegisterPressure::Set* usedByPhiNodes = NULL;
// Allocate the globals sets.
RegisterPressure::Set* liveIn = new(pool) RegisterPressure::Set[nNodes](pool, nameCount);
RegisterPressure::Set* liveOut = new(pool) RegisterPressure::Set[nNodes](pool, nameCount);
// First stage of the liveness analysis: Compute the sets LocalLive(stored in LiveIn) and Killed.
//
for (Uint32 n = 0; n < (nNodes - 1); n++) {
ControlNode& node = *nodes[n];
RegisterPressure::Set& currentLocalLive = liveIn[n];
RegisterPressure::Set& currentKilled = killed[n];
InstructionList& phiNodes = node.getPhiNodeInstructions();
if ((usedByPhiNodes == NULL) && !phiNodes.empty())
usedByPhiNodes = new(pool) RegisterPressure::Set[nNodes](pool, nameCount);
for (InstructionList::iterator p = phiNodes.begin(); !phiNodes.done(p); p = phiNodes.advance(p)) {
Instruction& phiNode = phiNodes.get(p);
InstructionDefine& define = phiNode.getInstructionDefineBegin()[0];
currentKilled.set(define.getRegisterName());
typedef DoublyLinkedList<ControlEdge> ControlEdgeList;
const ControlEdgeList& predecessors = node.getPredecessors();
ControlEdgeList::iterator p = predecessors.begin();
InstructionUse* useEnd = phiNode.getInstructionUseEnd();
for (InstructionUse* usePtr = phiNode.getInstructionUseBegin(); usePtr < useEnd; usePtr++, p = predecessors.advance(p))
if (usePtr->isRegister())
usedByPhiNodes[predecessors.get(p).getSource().dfsNum].set(usePtr->getRegisterName());
}
// Find the instructions contributions to the sets LocalLive and Killed.
//
InstructionList& instructions = node.getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
Instruction& instruction = instructions.get(i);
// If a VirtualRegister is 'used' before being 'defined' then we add it to set LocalLive.
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
Uint32 index = usePtr->getRegisterName();
if (!currentKilled.test(index))
currentLocalLive.set(index);
}
// If a Virtualregister is 'defined' then we add it to the set Killed.
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
currentKilled.set(definePtr->getRegisterName());
}
}
// Second stage of the liveness analysis: We propagate the LiveIn & LiveOut through the entire
// control-flow graph.
//
RegisterPressure::Set temp(pool, nameCount);
bool changed;
do {
changed = false;
// For all nodes is this graph except the endNode.
for (Int32 n = (nNodes - 2); n >= 0; n--) {
ControlNode& node = *nodes[n];
RegisterPressure::Set& currentLiveIn = liveIn[n];
RegisterPressure::Set& currentLiveOut = liveOut[n];
// Compute temp = Union of LiveIn(s) (s a successor of this node) | usedByPhiNodes(n).
// temp will be the new LiveOut(n).
Uint32 nSuccessors = node.nSuccessors();
if (nSuccessors != 0) {
temp = liveIn[node.nthSuccessor(0).getTarget().dfsNum];
for (Uint32 s = 1; s < nSuccessors; s++)
temp |= liveIn[node.nthSuccessor(s).getTarget().dfsNum];
} else
temp.clear();
// Insert the phiNodes contribution.
if (usedByPhiNodes != NULL)
temp |= usedByPhiNodes[n];
// If temp and LiveOut(n) differ then set LiveOut(n) = temp and recalculate the
// new LiveIn(n).
if (currentLiveOut != temp) {
currentLiveOut = temp;
temp -= killed[n]; // FIX: could be optimized with one call to unionDiff !
temp |= currentLiveIn;
if (currentLiveIn != temp) {
currentLiveIn = temp;
changed = true;
}
}
}
} while(changed);
LivenessInfo<RegisterPressure> liveness;
liveness.liveIn = liveIn;
liveness.liveOut = liveOut;
DEBUG_LOG_ONLY(liveness.size = nNodes);
return liveness;
}
#ifdef DEBUG_LOG
template <class RegisterPressure>
void LivenessInfo<RegisterPressure>::printPretty(LogModuleObject log)
{
for (Uint32 n = 0; n < size; n++) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("Node N%d:\n\tliveIn = ", n));
liveIn[n].printPretty(log);
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\tliveOut = "));
liveOut[n].printPretty(log);
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\n"));
}
}
#endif // DEBUG_LOG
#endif // _LIVENESS_H_

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@@ -1,40 +0,0 @@
#! gmake
DEPTH = ../..
MODULE_NAME = RegisterAllocator
include $(DEPTH)/config/config.mk
INCLUDES += \
-I$(DEPTH)/Utilities/General \
-I$(DEPTH)/Utilities/zlib \
-I$(DEPTH)/Runtime/ClassReader \
-I$(DEPTH)/Runtime/NativeMethods \
-I$(DEPTH)/Runtime/System \
-I$(DEPTH)/Runtime/ClassInfo \
-I$(DEPTH)/Runtime/FileReader \
-I$(DEPTH)/Compiler/PrimitiveGraph \
-I$(DEPTH)/Compiler/FrontEnd \
-I$(DEPTH)/Compiler/Optimizer \
-I$(DEPTH)/Compiler/CodeGenerator \
-I$(DEPTH)/Compiler/CodeGenerator/md \
-I$(DEPTH)/Compiler/CodeGenerator/md/$(CPU_ARCH) \
-I$(DEPTH)/Compiler/RegisterAllocator \
-I$(DEPTH)/Driver/StandAloneJava \
-I$(DEPTH)/Debugger \
$(NULL)
CXXSRCS = \
RegisterAllocator.cpp \
RegisterAllocatorTools.cpp \
DominatorGraph.cpp \
VirtualRegister.cpp \
BitSet.cpp \
SparseSet.cpp \
$(NULL)
include $(DEPTH)/config/rules.mk
libs:: $(MODULE)

View File

@@ -1,392 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _PHI_NODE_REMOVER_H_
#define _PHI_NODE_REMOVER_H_
#include "Fundamentals.h"
#include "Pool.h"
#include "ControlGraph.h"
#include "DominatorGraph.h"
#include "VirtualRegister.h"
#include "RegisterPressure.h"
#include "Liveness.h"
#include "Instruction.h"
#include "InstructionEmitter.h"
#include "SparseSet.h"
#include <string.h>
//------------------------------------------------------------------------------
// RegisterNameNode -
struct RegisterNameNode
{
RegisterNameNode* next;
RegisterName newName;
Uint32 nextPushed;
};
//------------------------------------------------------------------------------
// CopyData -
struct CopyData
{
RegisterName source;
RegisterClassKind classKind;
Uint32 useCount;
bool isLiveOut;
RegisterName sourceNameToUse;
RegisterName temporaryName;
RegisterNameNode* newName;
};
//------------------------------------------------------------------------------
// PhiNodeRemover<RegisterPressure> -
template <class RegisterPressure>
struct PhiNodeRemover
{
// Replace the phi nodes by copy instructions.
static void replacePhiNodes(ControlGraph& controlGraph, VirtualRegisterManager& vrManager, InstructionEmitter& emitter);
};
// Split some of the critical edges and return true if there are still some
// in the graph after that.
//
static bool splitCriticalEdges(ControlGraph& /*cg*/)
{
// FIX: not implemented.
return true;
}
inline void pushName(Pool& pool, RegisterNameNode** stack, SparseSet& pushed, Uint32* nodeListPointer, RegisterName oldName, RegisterName newName)
{
RegisterNameNode& newNode = *new(pool) RegisterNameNode();
if (pushed.test(oldName))
(*stack)->newName = newName;
else {
newNode.newName = newName;
newNode.nextPushed = *nodeListPointer;
*nodeListPointer = oldName;
newNode.next = *stack;
*stack = &newNode;
pushed.set(oldName);
}
}
template <class RegisterPressure>
void PhiNodeRemover<RegisterPressure>::replacePhiNodes(ControlGraph& controlGraph, VirtualRegisterManager& vrManager, InstructionEmitter& emitter)
{
Pool& pool = controlGraph.pool;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
// Initialize the local variables.
//
// When we insert the copies we will also need to create new VirtualRegisters for
// the insertion of temporaries. The maximum number of temporary register will not
// exceed the number of phiNodes in the primitive graph.
Uint32 nameCount = vrManager.getSize();
Uint32 maxNameCount = nameCount;
for (Uint32 n = 0; n < nNodes; n++)
maxNameCount += nodes[n]->getPhiNodes().length();
// If the CFG contains some critical edges (backward edge which source has more than one
// outgoing edge and destination has more than one incomimg edge) then we need the liveness
// information to be able to insert temporary copies.
RegisterPressure::Set* liveOut = NULL;
if (splitCriticalEdges(controlGraph))
liveOut = Liveness<LowRegisterPressure>::analysis(controlGraph, nameCount).liveOut;
DominatorGraph dGraph(controlGraph);
SparseSet pushed(pool, maxNameCount);
SparseSet destinationList(pool, maxNameCount);
SparseSet workList(pool, maxNameCount);
CopyData* copyStats = new(pool) CopyData[maxNameCount];
memset(copyStats, '\0', maxNameCount*sizeof(CopyData));
struct NodeStack {
Uint32* next;
Uint32* limit;
Uint32 pushedList;
};
// Allocate the node stack and initialize the node stack pointer.
NodeStack* nodeStack = new(pool) NodeStack[nNodes + 1];
NodeStack* nodeStackPtr = nodeStack;
// We start by the begin node.
Uint32 startNode = 0;
Uint32* next = &startNode;
Uint32* limit = &startNode + 1;
while (true) {
if (next == limit) {
// If there are no more node in the sibling, we have to pop the current
// frame from the stack and update the copyStats of the pushed nodes.
//
if (nodeStackPtr == nodeStack)
// We are at the bottom of the stack and there are no more nodes
// to look at. We are done !
break;
--nodeStackPtr;
// We are done with all the children of this node in the dominator tree.
// We need to update the copy information of all the new names pushed
// during the walk over this node.
Uint32 pushedList = nodeStackPtr->pushedList;
while (pushedList != 0) {
Uint32 nextName = copyStats[pushedList].newName->nextPushed;
copyStats[pushedList].newName = copyStats[pushedList].newName->next;
pushedList = nextName;
}
// restore the previous frame.
next = nodeStackPtr->next;
limit = nodeStackPtr->limit;
} else {
Uint32 currentNode = *next++;
Uint32 pushedList = 0;
// Initialize the sets.
pushed.clear();
destinationList.clear();
// STEP1:
// Walk the instruction list and to replace all the instruction uses with their new name.
// If the instruction is a phi node and its defined register is alive at the end of this
// block then we push the defined register into the stack.
//
ControlNode& node = *nodes[currentNode];
RegisterPressure::Set* currentLiveOut = (liveOut != NULL) ? &liveOut[currentNode] : (RegisterPressure::Set*) 0;
InstructionList& phiNodes = node.getPhiNodeInstructions();
for (InstructionList::iterator p = phiNodes.begin(); !phiNodes.done(p); p = phiNodes.advance(p)) {
Instruction& phiNode = phiNodes.get(p);
InstructionUse* useEnd = phiNode.getInstructionUseEnd();
for (InstructionUse* usePtr = phiNode.getInstructionUseBegin(); usePtr < useEnd; usePtr++) {
assert(usePtr->isRegister());
RegisterName name = usePtr->getRegisterName();
if (copyStats[name].newName != NULL && copyStats[name].newName->newName != name)
usePtr->setRegisterName(copyStats[name].newName->newName);
}
if (currentLiveOut != NULL) {
// This is a phi node and we have to push its defined name if it is live
// at the end of the node. We only need to do this if the CFG has critical edges.
assert(phiNode.getInstructionDefineBegin() != phiNode.getInstructionDefineEnd() && phiNode.getInstructionDefineBegin()[0].isRegister());
RegisterName name = phiNode.getInstructionDefineBegin()[0].getRegisterName();
if (currentLiveOut->test(name))
pushName(pool, &(copyStats[name].newName), pushed, &pushedList, name, name);
}
}
InstructionList& instructions = node.getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName name = usePtr->getRegisterName();
if (copyStats[name].newName != NULL && copyStats[name].newName->newName != name)
usePtr->setRegisterName(copyStats[name].newName->newName);
}
}
// STEP2:
// Look at this node's successors' phiNodes. We keep track of the number of time
// a VR will be used by another copy instruction and insert each definition into the
// destinationList. This is the only pass over this node's successors as we will
// get all the information we need in the CopyData structures.
//
ControlEdge* successorEdgeEnd = node.getSuccessorsEnd();
for (ControlEdge* successorEdgePtr = node.getSuccessorsBegin(); successorEdgePtr < successorEdgeEnd; successorEdgePtr++) {
Uint32 useIndex = successorEdgePtr->getIndex();
ControlNode& successor = successorEdgePtr->getTarget();
// Look at its phi nodes. The phi nodes are at the top of the instruction list. We exit
// as soon as we find an instruction which is not a phi node
InstructionList& phiNodes = successor.getPhiNodeInstructions();
for (InstructionList::iterator p = phiNodes.begin(); !phiNodes.done(p); p = phiNodes.advance(p)) {
Instruction& phiNode = phiNodes.get(p);
assert((phiNode.getInstructionUseBegin() + useIndex) < phiNode.getInstructionUseEnd());
assert(phiNode.getInstructionDefineBegin() != phiNode.getInstructionDefineEnd());
InstructionUse& source = phiNode.getInstructionUseBegin()[useIndex];
InstructionDefine& destination = phiNode.getInstructionDefineBegin()[0];
assert(source.isRegister() && destination.isRegister());
RegisterName sourceName = source.getRegisterName();
RegisterName destinationName = destination.getRegisterName();
// Get the correct name for the source.
if (copyStats[sourceName].newName != NULL)
sourceName = copyStats[sourceName].newName->newName;
// Update the CopyData structures.
if ((sourceName != rnInvalid) && (sourceName != destinationName)) {
copyStats[destinationName].source = sourceName;
copyStats[destinationName].classKind = destination.getRegisterClass();
copyStats[destinationName].isLiveOut = (currentLiveOut != NULL) ? currentLiveOut->test(destinationName) : false;
copyStats[destinationName].sourceNameToUse = destinationName;
copyStats[sourceName].sourceNameToUse = sourceName;
copyStats[sourceName].useCount++;
destinationList.set(destinationName);
}
}
}
// STEP3:
// Insert into the worklist only the destination registers that will be not used in
// another copy instruction in this block.
//
assert(workList.getSize() == 0);
for (SparseSet::iterator d = destinationList.begin(); !destinationList.done(d); d = destinationList.advance(d)) {
Uint32 dest = destinationList.get(d);
if (copyStats[dest].useCount == 0)
workList.set(dest);
}
// STEP4:
// Insert the copy instructions.
//
Uint32 destinationListSize = destinationList.getSize();
InstructionList::iterator endOfTheNode = instructions.end();
// Find the right place to insert the copy instructions.
if (destinationListSize != 0)
while (instructions.get(endOfTheNode).getFlags() & ifControl)
endOfTheNode = instructions.retreat(endOfTheNode);
while (destinationListSize != 0) {
while(workList.getSize()) {
RegisterName destinationName = RegisterName(workList.getOne());
RegisterName sourceName = copyStats[destinationName].source;
workList.clear(destinationName);
if (copyStats[destinationName].isLiveOut && !copyStats[destinationName].temporaryName) {
// Lost copy problem.
copyStats[destinationName].isLiveOut = false;
RegisterName sourceName = destinationName;
RegisterClassKind classKind = copyStats[sourceName].classKind;
RegisterName destinationName = getName(vrManager.newVirtualRegister(classKind));
assert(destinationName < maxNameCount);
copyStats[destinationName].classKind = classKind;
copyStats[sourceName].useCount = 0;
// We need to insert a copy to a temporary register to keep the
// source register valid at the end of the node defining it.
// This copy will be inserted right after the phi node defining it.
RegisterName from = copyStats[sourceName].sourceNameToUse;
Instruction* definingPhiNode = vrManager.getVirtualRegister(from).getDefiningInstruction();
assert(definingPhiNode && (definingPhiNode->getFlags() & ifPhiNode) != 0);
RegisterID fromID = buildRegisterID(from, classKind);
RegisterID toID = buildRegisterID(destinationName, classKind);
Instruction& copy = emitter.newCopy(*definingPhiNode->getPrimitive(), fromID, toID);
vrManager.getVirtualRegister(destinationName).setDefiningInstruction(copy);
definingPhiNode->getPrimitive()->getContainer()->getInstructions().addFirst(copy);
copyStats[sourceName].temporaryName = destinationName;
copyStats[sourceName].sourceNameToUse = destinationName;
pushName(pool, &(copyStats[sourceName].newName), pushed, &pushedList, sourceName, destinationName);
}
// Insert the copy instruction at the end of the current node.
RegisterName from = copyStats[sourceName].sourceNameToUse;
RegisterClassKind classKind = copyStats[destinationName].classKind;
RegisterID fromID = buildRegisterID(from, classKind);
RegisterID toID = buildRegisterID(destinationName, classKind);
Instruction& copy = emitter.newCopy(*vrManager.getVirtualRegister(from).getDefiningInstruction()->getPrimitive(), fromID, toID);
instructions.insertAfter(copy, endOfTheNode);
endOfTheNode = instructions.advance(endOfTheNode);
copyStats[sourceName].useCount = 0;
if (destinationList.test(sourceName) && copyStats[sourceName].isLiveOut)
pushName(pool, &(copyStats[sourceName].newName), pushed, &pushedList, sourceName, destinationName);
copyStats[sourceName].isLiveOut = false;
copyStats[sourceName].sourceNameToUse = destinationName;
if (destinationList.test(sourceName))
workList.set(sourceName);
destinationList.clear(destinationName);
}
destinationListSize = destinationList.getSize();
if (destinationListSize != 0) {
RegisterName sourceName = RegisterName(destinationList.getOne());
RegisterName destinationName;
if (!copyStats[sourceName].temporaryName) {
// Cycle problem.
RegisterClassKind classKind = copyStats[sourceName].classKind;
destinationName = getName(vrManager.newVirtualRegister(classKind));
assert(destinationName < maxNameCount);
copyStats[destinationName].classKind = classKind;
copyStats[sourceName].temporaryName = destinationName;
// Insert the copy instruction at the end of the current node.
RegisterName from = copyStats[sourceName].sourceNameToUse;
RegisterID fromID = buildRegisterID(from, classKind);
RegisterID toID = buildRegisterID(destinationName, classKind);
Instruction& copy = emitter.newCopy(*vrManager.getVirtualRegister(from).getDefiningInstruction()->getPrimitive(), fromID, toID);
vrManager.getVirtualRegister(destinationName).setDefiningInstruction(copy);
instructions.insertAfter(copy, endOfTheNode);
endOfTheNode = instructions.advance(endOfTheNode);
} else
destinationName = copyStats[sourceName].temporaryName;
copyStats[sourceName].useCount = 0;
copyStats[sourceName].isLiveOut = false;
copyStats[sourceName].sourceNameToUse = destinationName;
pushName(pool, &(copyStats[sourceName].newName), pushed, &pushedList, sourceName, destinationName);
workList.set(sourceName);
}
}
nodeStackPtr->pushedList = pushedList;
nodeStackPtr->next = next;
nodeStackPtr->limit = limit;
++nodeStackPtr;
next = dGraph.getSuccessorsBegin(currentNode);
limit = dGraph.getSuccessorsEnd(currentNode);
}
}
}
#endif // _PHI_NODE_REMOVER_H_

View File

@@ -1,155 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#include "Fundamentals.h"
#include "LogModule.h"
#include "RegisterAllocator.h"
#include "RegisterPressure.h"
#include "RegisterAllocatorTools.h"
#include "PhiNodeRemover.h"
#include "LiveRange.h"
#include "Liveness.h"
#include "InterferenceGraph.h"
#include "LiveRangeGraph.h"
#include "Coalescing.h"
#include "Spilling.h"
#include "Coloring.h"
#include "Splits.h"
class Pool;
class ControlGraph;
class VirtualRegisterManager;
class InstructionEmitter;
UT_DEFINE_LOG_MODULE(RegAlloc);
void RegisterAllocator::allocateRegisters(Pool& pool, ControlGraph& controlGraph, VirtualRegisterManager& vrManager, InstructionEmitter& emitter)
{
// Insert the phi node instructions. We want to do this to have a single defined register per instruction.
// If we keep the PhiNode (as a DataNode) and a PhiNode is of DoubleWordKind then we have to execute
// some special code for the high word annotation.
//
RegisterAllocatorTools::insertPhiNodeInstructions(controlGraph, emitter);
// Perform some tests on the instruction graph.
//
DEBUG_ONLY(RegisterAllocatorTools::testTheInstructionGraph(controlGraph, vrManager));
// Replace the phi node instructions by their equivalent copy instructions.
//
PhiNodeRemover<LowRegisterPressure>::replacePhiNodes(controlGraph, vrManager, emitter);
// Do the register allocation.
//
RegisterAllocator registerAllocator(pool, controlGraph, vrManager, emitter);
registerAllocator.doGraphColoring();
}
void RegisterAllocator::doGraphColoring()
{
// Initialize the liverange map.
//
initLiveRanges();
// Build the live ranges. We do this to compress the number of RegisterNames
// used in the insterference graph.
//
LiveRange<LowRegisterPressure>::build(*this);
// Remove unnecessary copies.
//
RegisterAllocatorTools::removeUnnecessaryCopies(*this);
for (Uint8 loop = 0; loop < 10; loop++) {
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("********* RegisterAllocator loop %d *********\n", loop));
while(true) {
// Build the interference graph.
//
iGraph.build();
// Coalesce the copy instructions.
//
if (!Coalescing<LowRegisterPressure>::coalesce(*this))
break;
}
// Print the interference graph.
//
DEBUG_LOG_ONLY(iGraph.printPretty(UT_LOG_MODULE(RegAlloc)));
// Calculate the spill costs.
//
Spilling<LowRegisterPressure>::calculateSpillCosts(*this);
DEBUG_LOG_ONLY(RegisterAllocatorTools::printSpillCosts(*this));
// Calculate the split costs.
//
Splits<LowRegisterPressure>::calculateSplitCosts(*this);
DEBUG_LOG_ONLY(RegisterAllocatorTools::printSplitCosts(*this));
// Build the live range graph.
//
lGraph.build();
DEBUG_LOG_ONLY(lGraph.printPretty(UT_LOG_MODULE(RegAlloc)));
// Color the graph. If it succeeds then we're done with the
// register allocation.
//
if (Coloring<LowRegisterPressure>::color(*this)) {
// Write the final colors in the instruction graph.
//
Coloring<LowRegisterPressure>::finalColoring(*this);
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("********** RegisterAllocator done **********\n"));
DEBUG_LOG_ONLY(RegisterAllocatorTools::printInstructions(*this));
return;
}
// We need to spill some registers.
//
Spilling<LowRegisterPressure>::insertSpillCode(*this);
// Insert the split instructions.
//
Splits<LowRegisterPressure>::insertSplitCode(*this);
// Update the live ranges.
//
// FIX
}
#ifdef DEBUG_LOG
RegisterAllocatorTools::updateInstructionGraph(*this);
RegisterAllocatorTools::printInstructions(*this);
#endif
fprintf(stderr, "!!! Coloring failed after 10 loops !!!\n");
abort();
}
void RegisterAllocator::initLiveRanges()
{
Uint32 count = this->nameCount;
RegisterName* name2range = new(pool) RegisterName[nameCount];
for (RegisterName r = RegisterName(1); r < count; r = RegisterName(r + 1))
name2range[r] = r;
this->name2range = name2range;
rangeCount = count;
}

View File

@@ -1,88 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _REGISTER_ALLOCATOR_H_
#define _REGISTER_ALLOCATOR_H_
class Pool;
class ControlGraph;
class InstructionEmitter;
struct SpillCost;
struct SplitCost;
#include "Liveness.h"
#include "VirtualRegister.h"
#include "RegisterPressure.h" // This should included by Backend.cpp
#include "InterferenceGraph.h"
#include "LiveRangeGraph.h"
//template <class RegisterPressure>
class RegisterAllocator
{
public:
Pool& pool; //
ControlGraph& controlGraph; //
VirtualRegisterManager& vrManager; //
InstructionEmitter& emitter; //
RegisterName* name2range; //
RegisterName* color; //
SpillCost* spillCost; //
SparseSet* willSpill; //
SplitCost* splitCost; //
NameLinkedList** splitAround; //
InterferenceGraph<LowRegisterPressure> iGraph; //
LiveRangeGraph<LowRegisterPressure> lGraph; //
LivenessInfo<LowRegisterPressure> liveness; //
Uint32 nameCount; //
Uint32 rangeCount; //
bool splitFound; //
private:
//
//
void doGraphColoring();
public:
//
//
inline RegisterAllocator(Pool& pool, ControlGraph& controlGraph, VirtualRegisterManager& vrManager, InstructionEmitter& emitter);
//
//
bool canInterfere(RegisterName /*name1*/, RegisterName /*name2*/) const {return true;}
//
//
void initLiveRanges();
//
//
static void allocateRegisters(Pool& pool, ControlGraph& controlGraph, VirtualRegisterManager& vrManager, InstructionEmitter& emitter);
};
//
//
inline RegisterAllocator::RegisterAllocator(Pool& pool, ControlGraph& controlGraph, VirtualRegisterManager& vrManager, InstructionEmitter& emitter)
: pool(pool), controlGraph(controlGraph), vrManager(vrManager), emitter(emitter), iGraph(*this), lGraph(*this), nameCount(vrManager.getSize()) {}
#endif // _REGISTER_ALLOCATOR_H_

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@@ -1,355 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#include "Fundamentals.h"
#include "LogModule.h"
#include "RegisterAllocatorTools.h"
#include "Pool.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Primitives.h"
#include "InstructionEmitter.h"
#include "Instruction.h"
#include "RegisterAllocator.h"
#include "Spilling.h"
#include "Splits.h"
#include "BitSet.h"
UT_EXTERN_LOG_MODULE(RegAlloc);
#ifdef DEBUG
void RegisterAllocatorTools::testTheInstructionGraph(ControlGraph& controlGraph, VirtualRegisterManager& vrManager)
{
// Test the declared VirtualRegisters. The register allocator tries to condense the register universe.
// Any gap in the VirtualRegister names will be a loss of efficiency !!!!
Uint32 nameCount = vrManager.getSize();
BitSet registerSeen(controlGraph.pool, nameCount);
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
for (Uint32 n = 0; n < nNodes; n++) {
InstructionList& instructions = nodes[n]->getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
registerSeen.set(usePtr->getRegisterName());
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
registerSeen.set(definePtr->getRegisterName());
}
InstructionList& phiNodes = nodes[n]->getPhiNodeInstructions();
for (InstructionList::iterator p = phiNodes.begin(); !phiNodes.done(p); p = phiNodes.advance(p)) {
Instruction& instruction = phiNodes.get(p);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
registerSeen.set(usePtr->getRegisterName());
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
registerSeen.set(definePtr->getRegisterName());
}
}
bool renameRegisters = false;
for (BitSet::iterator i = registerSeen.nextZero(0); !registerSeen.done(i); i = registerSeen.nextZero(i)) {
renameRegisters = true;
fprintf(stderr,
"WARNING: The VirtualRegister vr%d has been allocated during CodeGeneration but\n"
" is never used nor defined by any instruction in the instruction graph\n"
" PLEASE FIX \n",
i);
}
if (renameRegisters) {
Instruction** definingInstruction = new Instruction*[nameCount];
memset(definingInstruction, '\0', nameCount * sizeof(Instruction*));
RegisterName* newName = new RegisterName[nameCount];
memset(newName, '\0', nameCount * sizeof(RegisterName));
RegisterName nextName = RegisterName(1);
for (Uint32 n = 0; n < nNodes; n++) {
InstructionList& instructions = nodes[n]->getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName name = usePtr->getRegisterName();
if (newName[name] == rnInvalid) {
newName[name] = nextName;
definingInstruction[nextName] = vrManager.getVirtualRegister(name).getDefiningInstruction();
nextName = RegisterName(nextName + 1);
}
usePtr->setRegisterName(newName[name]);
}
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
RegisterName name = definePtr->getRegisterName();
if (newName[name] == rnInvalid) {
newName[name] = nextName;
definingInstruction[nextName] = vrManager.getVirtualRegister(name).getDefiningInstruction();
nextName = RegisterName(nextName + 1);
}
definePtr->setRegisterName(newName[name]);
}
}
InstructionList& phiNodes = nodes[n]->getPhiNodeInstructions();
for (InstructionList::iterator p = phiNodes.begin(); !phiNodes.done(p); p = phiNodes.advance(p)) {
Instruction& instruction = phiNodes.get(p);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName name = usePtr->getRegisterName();
if (newName[name] == rnInvalid) {
newName[name] = nextName;
definingInstruction[nextName] = vrManager.getVirtualRegister(name).getDefiningInstruction();
nextName = RegisterName(nextName + 1);
}
usePtr->setRegisterName(newName[name]);
}
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
RegisterName name = definePtr->getRegisterName();
if (newName[name] == rnInvalid) {
newName[name] = nextName;
definingInstruction[nextName] = vrManager.getVirtualRegister(name).getDefiningInstruction();
nextName = RegisterName(nextName + 1);
}
definePtr->setRegisterName(newName[name]);
}
}
}
vrManager.setSize(nextName);
for (RegisterName r = RegisterName(1); r < nextName; r = RegisterName(r + 1))
vrManager.getVirtualRegister(r).definingInstruction = definingInstruction[r];
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("RegisterMap:\n"));
for (Uint32 i = 1; i < nameCount; i++)
if (newName[i] != 0)
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\tvr%d becomes vr%d.\n", i, newName[i]));
else
UT_OBJECTLOG(UT_LOG_MODULE(RegAlloc), PR_LOG_ALWAYS, ("\tvr%d is dead.\n", i));
delete newName;
delete definingInstruction;
}
}
#endif // DEBUG
void RegisterAllocatorTools::removeUnnecessaryCopies(RegisterAllocator& registerAllocator)
{
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
RegisterName* name2range = registerAllocator.name2range;
for (Uint32 n = 0; n < nNodes; n++) {
InstructionList& instructions = nodes[n]->getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i);) {
Instruction& instruction = instructions.get(i);
i = instructions.advance(i);
if (instruction.getFlags() & ifCopy) {
assert(instruction.getInstructionUseBegin() != instruction.getInstructionUseEnd() && instruction.getInstructionUseBegin()[0].isRegister());
assert(instruction.getInstructionDefineBegin() != instruction.getInstructionDefineEnd() && instruction.getInstructionDefineBegin()[0].isRegister());
RegisterName source = name2range[instruction.getInstructionUseBegin()[0].getRegisterName()];
RegisterName destination = name2range[instruction.getInstructionDefineBegin()[0].getRegisterName()];
if (source == destination)
instruction.remove();
}
}
}
}
void RegisterAllocatorTools::updateInstructionGraph(RegisterAllocator& registerAllocator)
{
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
RegisterName* name2range = registerAllocator.name2range;
for (Uint32 n = 0; n < nNodes; n++) {
InstructionList& instructions = nodes[n]->getInstructions();
for (InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
usePtr->setRegisterName(name2range[usePtr->getRegisterName()]);
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
definePtr->setRegisterName(name2range[definePtr->getRegisterName()]);
}
InstructionList& phiNodes = nodes[n]->getPhiNodeInstructions();
for (InstructionList::iterator p = phiNodes.begin(); !phiNodes.done(p); p = phiNodes.advance(p)) {
Instruction& instruction = phiNodes.get(p);
InstructionUse* useEnd = instruction.getInstructionUseEnd();
for (InstructionUse* usePtr = instruction.getInstructionUseBegin(); usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
usePtr->setRegisterName(name2range[usePtr->getRegisterName()]);
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
for (InstructionDefine* definePtr = instruction.getInstructionDefineBegin(); definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
definePtr->setRegisterName(name2range[definePtr->getRegisterName()]);
}
}
}
void RegisterAllocatorTools::insertPhiNodeInstructions(ControlGraph& controlGraph, InstructionEmitter& emitter)
{
Pool& pool = controlGraph.pool;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
for (Uint32 n = 0; n < nNodes; n++) {
ControlNode& node = *nodes[n];
DoublyLinkedList<PhiNode>& phiNodes = node.getPhiNodes();
if (!phiNodes.empty()) {
// Set the index of the incoming edges.
Uint32 index = 0;
const DoublyLinkedList<ControlEdge>& predecessors = node.getPredecessors();
for (DoublyLinkedList<ControlEdge>::iterator p = predecessors.begin(); !predecessors.done(p); p = predecessors.advance(p))
predecessors.get(p).setIndex(index++);
// Insert the phi node instruction in the instruction list.
for (DoublyLinkedList<PhiNode>::iterator i = phiNodes.begin(); !phiNodes.done(i); i = phiNodes.advance(i)) {
PhiNode& phiNode = phiNodes.get(i);
ValueKind kind = phiNode.getKind();
if (!isStorableKind(kind))
continue;
RegisterClassKind classKind = rckGeneral; // FIX: get class kind from phi node kind.
Uint32 nInputs = phiNode.nInputs();
PhiNodeInstruction& phiNodeInstruction = *new(pool) PhiNodeInstruction(&phiNode, pool, nInputs);
emitter.defineProducer(phiNode, phiNodeInstruction, 0, classKind, drLow);
for (Uint32 whichInput = 0; whichInput < nInputs; whichInput++)
emitter.useProducer(phiNode.nthInputVariable(whichInput), phiNodeInstruction, whichInput, classKind, drLow);
node.addPhiNodeInstruction(phiNodeInstruction);
if (isDoublewordKind(kind)) {
PhiNodeInstruction& phiNodeInstruction = *new(pool) PhiNodeInstruction(&phiNode, pool, nInputs);
emitter.defineProducer(phiNode, phiNodeInstruction, 0, classKind, drHigh);
for (Uint32 whichInput = 0; whichInput < nInputs; whichInput++)
emitter.useProducer(phiNode.nthInputVariable(whichInput), phiNodeInstruction, whichInput, classKind, drHigh);
node.addPhiNodeInstruction(phiNodeInstruction);
}
}
}
}
}
#ifdef DEBUG_LOG
void RegisterAllocatorTools::printSpillCosts(RegisterAllocator& registerAllocator)
{
LogModuleObject log = UT_LOG_MODULE(RegAlloc);
Uint32 rangeCount = registerAllocator.rangeCount;
SpillCost* cost = registerAllocator.spillCost;
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("Spill costs:\n"));
for (Uint32 i = 1; i < rangeCount; i++) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\trange %d : ", i));
if (cost[i].infinite)
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("infinite\n"));
else
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("%f\n", cost[i].cost));
}
}
void RegisterAllocatorTools::printSplitCosts(RegisterAllocator& registerAllocator)
{
LogModuleObject log = UT_LOG_MODULE(RegAlloc);
Uint32 rangeCount = registerAllocator.rangeCount;
SplitCost* cost = registerAllocator.splitCost;
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("Split costs:\n"));
for (Uint32 i = 1; i < rangeCount; i++) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\trange %d : loads = %f stores = %f\n", i, cost[i].loads, cost[i].stores));
}
}
void RegisterAllocatorTools::printInstructions(RegisterAllocator& registerAllocator)
{
LogModuleObject log = UT_LOG_MODULE(RegAlloc);
ControlNode** nodes = registerAllocator.controlGraph.dfsList;
Uint32 nNodes = registerAllocator.controlGraph.nNodes;
for (Uint32 n = 0; n < nNodes; n++) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("N%d:\n", n));
InstructionList& phiNodes = nodes[n]->getPhiNodeInstructions();
InstructionList& instructions = nodes[n]->getInstructions();
if (!phiNodes.empty()) {
UT_OBJECTLOG(log, PR_LOG_ALWAYS, (" PhiNodes:\n", n));
for(InstructionList::iterator i = phiNodes.begin(); !phiNodes.done(i); i = phiNodes.advance(i)) {
phiNodes.get(i).printPretty(log);
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\n"));
}
if (!instructions.empty())
UT_OBJECTLOG(log, PR_LOG_ALWAYS, (" Instructions:\n", n));
}
for(InstructionList::iterator i = instructions.begin(); !instructions.done(i); i = instructions.advance(i)) {
instructions.get(i).printPretty(log);
UT_OBJECTLOG(log, PR_LOG_ALWAYS, ("\n"));
}
}
}
#endif // DEBUG_LOG

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@@ -1,117 +0,0 @@
// -*- mode:C++; tab-width:4; truncate-lines:t -*-
//
// CONFIDENTIAL AND PROPRIETARY SOURCE CODE OF
// NETSCAPE COMMUNICATIONS CORPORATION
// Copyright © 1996, 1997 Netscape Communications Corporation. All Rights
// Reserved. Use of this Source Code is subject to the terms of the
// applicable license agreement from Netscape Communications Corporation.
// The copyright notice(s) in this Source Code does not indicate actual or
// intended publication of this Source Code.
//
// $Id: RegisterAllocatorTools.h,v 1.1.2.1 1999-03-02 16:12:05 fur%netscape.com Exp $
//
#ifndef _REGISTER_ALLOCATOR_TOOLS_H_
#define _REGISTER_ALLOCATOR_TOOLS_H_
#include "LogModule.h"
#include "RegisterTypes.h"
#include <string.h>
class RegisterAllocator;
class ControlGraph;
class InstructionEmitter;
class VirtualRegisterManager;
struct RegisterAllocatorTools
{
//
//
static void insertPhiNodeInstructions(ControlGraph& controlGraph, InstructionEmitter& emitter);
//
//
static void updateInstructionGraph(RegisterAllocator& registerAllocator);
//
//
static void removeUnnecessaryCopies(RegisterAllocator& registerAllocator);
#ifdef DEBUG
//
//
static void testTheInstructionGraph(ControlGraph& controlGraph, VirtualRegisterManager& vrManager);
#endif // DEBUG
#ifdef DEBUG_LOG
//
//
static void printInstructions(RegisterAllocator& registerAllocator);
//
//
static void printSpillCosts(RegisterAllocator& registerAllocator);
//
//
static void printSplitCosts(RegisterAllocator& registerAllocator);
#endif // DEBUG_LOG
};
//
// FIX: this should go in a class (LookupTable ?)
//
inline RegisterName findRoot(RegisterName name, RegisterName* table)
{
RegisterName* stack = table;
RegisterName* stackPtr = stack;
RegisterName newName;
while((newName = table[name]) != name) {
*--stackPtr = name;
name = newName;
}
while (stackPtr != stack)
table[*stackPtr++] = name;
return name;
}
inline void init(RegisterName* table, Uint32 nameCount)
{
for (RegisterName r = RegisterName(0); r < nameCount; r = RegisterName(r + 1))
table[r] = r;
}
inline Uint32 compress(RegisterName* name2range, RegisterName* table, Uint32 nameCount, Uint32 tableSize)
{
RegisterName* liveRange = new RegisterName[tableSize];
memset(liveRange, '\0', tableSize * sizeof(RegisterName));
// Update the lookup table.
for (RegisterName r = RegisterName(1); r < tableSize; r = RegisterName(r + 1))
findRoot(r, table);
// Count the liveranges.
Uint32 liveRangeCount = 1;
for (RegisterName s = RegisterName(1); s < tableSize; s = RegisterName(s + 1))
if (table[s] == s)
liveRange[s] = RegisterName(liveRangeCount++);
for (RegisterName t = RegisterName(1); t < nameCount; t = RegisterName(t + 1))
name2range[t] = liveRange[table[name2range[t]]];
return liveRangeCount;
}
inline double doLog10(Uint32 power)
{
double log = 1.0;
while (power--)
log *= 10.0;
return log;
}
#endif // _REGISTER_ALLOCATOR_TOOLS_H_

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@@ -1,104 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _REGISTER_TYPES_H_
#define _REGISTER_TYPES_H_
#include "Fundamentals.h"
//------------------------------------------------------------------------------
// RegisterName -
//
enum RegisterName {
rnInvalid = 0,
};
//------------------------------------------------------------------------------
// RegisterClassKind -
//
enum RegisterClassKind {
rckInvalid = 0,
rckGeneral,
rckStackSlot,
nRegisterClassKind
};
//------------------------------------------------------------------------------
// RegisterID -
//
enum RegisterID {
invalidID = 0
};
//------------------------------------------------------------------------------
// RegisterKind -
//
enum RegisterKind {
rkCallerSave = 0,
rkCalleeSave,
};
struct NameLinkedList {
RegisterName name;
NameLinkedList* next;
};
#ifdef DEBUG
const registerNameMask = 0x03ffffff;
const coloredRegisterMask = 0x04000000;
const machineRegisterMask = 0x08000000;
const registerClassMask = 0xf0000000;
const registerNameShift = 0;
const coloredRegisterShift = 26;
const machineRegisterShift = 27;
const registerClassShift = 28;
#else // DEBUG
const registerNameMask = 0x0fffffff;
const registerClassMask = 0xf0000000;
const registerNameShift = 0;
const registerClassShift = 28;
#endif // DEBUG
inline RegisterClassKind getClass(RegisterID registerID) {return RegisterClassKind((registerID & registerClassMask) >> registerClassShift);}
inline RegisterName getName(RegisterID registerID) {return RegisterName((registerID & registerNameMask) >> registerNameShift);}
inline void setClass(RegisterID& registerID, RegisterClassKind classKind) {registerID = RegisterID((registerID & ~registerClassMask) | ((classKind << registerClassShift) & registerClassMask));}
inline void setName(RegisterID& registerID, RegisterName name) {assert((name & ~registerNameMask) == 0); registerID = RegisterID((registerID & ~registerNameMask) | ((name << registerNameShift) & registerNameMask));}
inline RegisterID buildRegisterID(RegisterName name, RegisterClassKind classKind) {return RegisterID(((classKind << registerClassShift) & registerClassMask) | ((name << registerNameShift) & registerNameMask));}
#ifdef DEBUG
inline bool isMachineRegister(RegisterID rid) {return (rid & machineRegisterMask) != 0;}
inline void setMachineRegister(RegisterID& rid) {rid = RegisterID(rid | machineRegisterMask);}
inline bool isColoredRegister(RegisterID rid) {return (rid & coloredRegisterMask) != 0;}
inline void setColoredRegister(RegisterID& rid) {rid = RegisterID(rid | coloredRegisterMask);}
#endif // DEBUG
#endif // _REGISTER_TYPES_H_

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@@ -1,168 +0,0 @@
// -*- mode:C++; tab-width:4; truncate-lines:t -*-
//
// CONFIDENTIAL AND PROPRIETARY SOURCE CODE OF
// NETSCAPE COMMUNICATIONS CORPORATION
// Copyright © 1996, 1997 Netscape Communications Corporation. All Rights
// Reserved. Use of this Source Code is subject to the terms of the
// applicable license agreement from Netscape Communications Corporation.
// The copyright notice(s) in this Source Code does not indicate actual or
// intended publication of this Source Code.
//
// $Id: SparseSet.h,v 1.1.2.1 1999-03-02 16:12:07 fur%netscape.com Exp $
//
#ifndef _SPARSE_SET_H_
#define _SPARSE_SET_H_
#include "Fundamentals.h"
#include "Pool.h"
#include "LogModule.h"
#include "BitSet.h"
class SparseSet
{
private:
struct Node {
Uint32 element;
Uint32 stackIndex;
};
Node* node;
Uint32 count;
Uint32 universeSize;
private:
// No copy constructor.
SparseSet(const SparseSet&);
// Check if the given set's universe is of the same size than this universe.
void checkUniverseCompatibility(const SparseSet& set) const {assert(set.universeSize == universeSize);}
// Check if pos is valid for this set's universe.
void checkMember(Int32 pos) const {assert(pos >=0 && Uint32(pos) < universeSize);}
public:
SparseSet(Pool& pool, Uint32 universeSize) : universeSize(universeSize) {node = new(pool) Node[universeSize]; clear();}
// Clear the sparse set.
void clear() {count = 0;}
// Clear the element at index.
inline void clear(Uint32 index);
// Set the element at index.
inline void set(Uint32 index);
// Return true if the element at index is set.
inline bool test(Uint32 index) const;
// Union with the given sparse set.
inline void or(const SparseSet& set);
// Intersection with the given sparse set.
inline void and(const SparseSet& set);
// Difference with the given sparse set.
inline void difference(const SparseSet& set);
// Copy set.
inline SparseSet& operator = (const SparseSet& set);
inline SparseSet& operator = (const BitSet& set);
// Return true if the sparse sets are identical.
friend bool operator == (const SparseSet& set1, const SparseSet& set2);
// Return true if the sparse sets are different.
friend bool operator != (const SparseSet& set1, const SparseSet& set2);
// Logical operators.
SparseSet& operator |= (const SparseSet& set) {or(set); return *this;}
SparseSet& operator &= (const SparseSet& set) {and(set); return *this;}
SparseSet& operator -= (const SparseSet& set) {difference(set); return *this;}
// Iterator to conform with the set API.
typedef Int32 iterator;
// Return the iterator for the first element of this set.
iterator begin() const {return count - 1;}
// Return the next iterator.
iterator advance(iterator pos) const {return --pos;}
// Return true if the iterator is at the end of the set.
bool done(iterator pos) const {return pos < 0;}
// Return the element for the given iterator;
Uint32 get(iterator pos) const {return node[pos].element;}
// Return one element of this set.
Uint32 getOne() const {assert(count > 0); return node[0].element;}
// Return the size of this set.
Uint32 getSize() const {return count;}
#ifdef DEBUG_LOG
// Print the set.
void printPretty(LogModuleObject log);
#endif // DEBUG_LOG
};
inline void SparseSet::clear(Uint32 element)
{
checkMember(element);
Uint32 count = this->count;
Node* node = this->node;
Uint32 stackIndex = node[element].stackIndex;
if ((stackIndex < count) && (node[stackIndex].element == element)) {
Uint32 stackTop = node[count - 1].element;
node[stackIndex].element = stackTop;
node[stackTop].stackIndex = stackIndex;
this->count = count - 1;
}
}
inline void SparseSet::set(Uint32 element)
{
checkMember(element);
Uint32 count = this->count;
Node* node = this->node;
Uint32 stackIndex = node[element].stackIndex;
if ((stackIndex >= count) || (node[stackIndex].element != element)) {
node[count].element = element;
node[element].stackIndex = count;
this->count = count + 1;
}
}
inline bool SparseSet::test(Uint32 element) const
{
checkMember(element);
Node* node = this->node;
Uint32 stackIndex = node[element].stackIndex;
return ((stackIndex < count) && (node[stackIndex].element == element));
}
inline SparseSet& SparseSet::operator = (const SparseSet& set)
{
checkUniverseCompatibility(set);
Uint32 sourceCount = set.getSize();
Node* node = this->node;
memcpy(node, set.node, sourceCount * sizeof(Node));
for (Uint32 i = 0; i < sourceCount; i++) {
Uint32 element = node[i].element;
node[element].stackIndex = i;
}
count = sourceCount;
return *this;
}
inline SparseSet& SparseSet::operator = (const BitSet& set)
{
// FIX: there's room for optimization here.
assert(universeSize == set.getSize());
clear();
for (Int32 i = set.firstOne(); i != -1; i = set.nextOne(i))
this->set(i);
return *this;
}
#endif // _SPARSE_SET_H_

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@@ -1,270 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef NEW_LAURENTM_CODE
#define INCLUDE_EMITTER
#include "CpuInfo.h"
#include "Fundamentals.h"
#include "ControlNodes.h"
#include "Instruction.h"
#include "InstructionEmitter.h"
#include "Spilling.h"
void Spilling::
insertSpillCode(ControlNode** dfsList, Uint32 nNodes)
{
PRUint32 nVirtualRegisters = vRegManager.count();
FastBitSet currentLive(vRegManager.pool, nVirtualRegisters);
FastBitSet usedInThisInstruction(vRegManager.pool, nVirtualRegisters);
RegisterFifo grNeedLoad(nVirtualRegisters);
RegisterFifo fpNeedLoad(nVirtualRegisters);
for (PRInt32 n = nNodes - 1; n >= 0; n--)
{
PR_ASSERT(grNeedLoad.empty() & fpNeedLoad.empty());
ControlNode& node = *dfsList[n];
currentLive = node.liveAtEnd;
PRUint32 nGeneralAlive = 0;
PRUint32 nFloatingPointAlive = 0;
// Get the number of registers alive at the end of this node.
for (PRInt32 j = currentLive.firstOne(); j != -1; j = currentLive.nextOne(j))
{
VirtualRegister& vReg = vRegManager.getVirtualRegister(j);
if (vReg.spillInfo.willSpill)
{
currentLive.clear(j);
}
else
{
switch (vReg.getClass())
{
case vrcInteger:
nGeneralAlive++;
break;
case vrcFloatingPoint:
case vrcFixedPoint:
nFloatingPointAlive++;
break;
default:
break;
}
}
}
// if(node.dfsNum == 8) printf("\n________Begin Node %d________\n", node.dfsNum);
InstructionList& instructions = node.getInstructions();
for (InstructionList::iterator i = instructions.end(); !instructions.done(i); i = instructions.retreat(i))
{
Instruction& instruction = instructions.get(i);
InstructionUse* useBegin = instruction.getInstructionUseBegin();
InstructionUse* useEnd = instruction.getInstructionUseEnd();
InstructionUse* usePtr;
InstructionDefine* defBegin = instruction.getInstructionDefineBegin();
InstructionDefine* defEnd = instruction.getInstructionDefineEnd();
InstructionDefine* defPtr;
// if(node.dfsNum == 8) { printf("\n");
// instruction.printPretty(stdout);
// printf("\n"); }
// Handle definitions
for (defPtr = defBegin; defPtr < defEnd; defPtr++)
if (defPtr->isVirtualRegister())
{
VirtualRegister& vReg = defPtr->getVirtualRegister();
currentLive.clear(vReg.getRegisterIndex());
switch (vReg.getClass())
{
case vrcInteger:
nGeneralAlive--;
break;
case vrcFloatingPoint:
case vrcFixedPoint:
nFloatingPointAlive--;
break;
default:
break;
}
}
// Check for deaths
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isVirtualRegister())
{
VirtualRegister& vReg = usePtr->getVirtualRegister();
if (!currentLive.test(vReg.getRegisterIndex()))
// This is the last use of this register.
{
currentLive.set(vReg.getRegisterIndex());
switch (vReg.getClass())
{
case vrcInteger:
nGeneralAlive++;
while (/*(nGeneralAlive > NUMBER_OF_GREGISTERS) &&*/ !grNeedLoad.empty())
{
PRUint32 toLoad = grNeedLoad.get();
currentLive.clear(toLoad);
nGeneralAlive--;
VirtualRegister& nReg = vRegManager.getVirtualRegister(toLoad);
Instruction& lastUsingInstruction = *nReg.spillInfo.lastUsingInstruction;
emitter.emitLoadAfter(*lastUsingInstruction.getPrimitive(), lastUsingInstruction.getLinks().prev,
nReg.getAlias(), *nReg.equivalentRegister[vrcStackSlot]);
nReg.releaseSelf();
}
break;
case vrcFloatingPoint:
case vrcFixedPoint:
nFloatingPointAlive++;
while (/*(nFloatingPointAlive > NUMBER_OF_FPREGISTERS) &&*/ !fpNeedLoad.empty())
{
PRUint32 toLoad = fpNeedLoad.get();
currentLive.clear(toLoad);
nFloatingPointAlive--;
VirtualRegister& nReg = vRegManager.getVirtualRegister(toLoad);
Instruction& lastUsingInstruction = *nReg.spillInfo.lastUsingInstruction;
emitter.emitLoadAfter(*lastUsingInstruction.getPrimitive(), lastUsingInstruction.getLinks().prev,
nReg.getAlias(), *nReg.equivalentRegister[vrcStackSlot]);
nReg.releaseSelf();
}
break;
default:
break;
}
}
}
// Handle uses
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isVirtualRegister())
{
VirtualRegister& vReg = usePtr->getVirtualRegister();
PRUint32 registerIndex = vReg.getRegisterIndex();
if (vReg.spillInfo.willSpill) {
#if defined(GENERATE_FOR_X86)
if (!instruction.switchUseToSpill((usePtr - useBegin), *vReg.equivalentRegister[vrcStackSlot]))
#endif
{
switch (vReg.getClass())
{
case vrcInteger:
if (!grNeedLoad.test(registerIndex))
{
grNeedLoad.put(registerIndex);
VirtualRegister& alias = vRegManager.newVirtualRegister(vrcInteger);
if (vReg.isPreColored())
alias.preColorRegister(vReg.getPreColor());
/* if (vReg.hasSpecialInterference) {
alias.specialInterference.sizeTo(NUMBER_OF_REGISTERS);
alias.specialInterference = vReg.specialInterference;
alias.hasSpecialInterference = true;
} */
vReg.setAlias(alias);
vReg.retainSelf();
}
break;
case vrcFloatingPoint:
case vrcFixedPoint:
if (!fpNeedLoad.test(registerIndex))
{
fpNeedLoad.put(registerIndex);
VirtualRegister& alias = vRegManager.newVirtualRegister(vReg.getClass());
if (vReg.isPreColored())
alias.preColorRegister(vReg.getPreColor());
/*if (vReg.hasSpecialInterference) {
alias.specialInterference.sizeTo(NUMBER_OF_REGISTERS);
alias.specialInterference = vReg.specialInterference;
alias.hasSpecialInterference = true;
} */
vReg.setAlias(alias);
vReg.retainSelf();
}
break;
default:
break;
}
usePtr->getVirtualRegisterPtr().initialize(vReg.getAlias());
usedInThisInstruction.set(registerIndex);
vReg.spillInfo.lastUsingInstruction = &instruction;
}
currentLive.clear(registerIndex);
} else { // will not spill
currentLive.set(registerIndex);
}
}
// Handle definitions
for (defPtr = defBegin; defPtr < defEnd; defPtr++)
if (defPtr->isVirtualRegister())
{
VirtualRegister& vReg = defPtr->getVirtualRegister();
if (vReg.spillInfo.willSpill)
#if defined(GENERATE_FOR_X86)
if (!instruction.switchDefineToSpill((defPtr - defBegin), *vReg.equivalentRegister[vrcStackSlot]))
#endif
{
if (usedInThisInstruction.test(vReg.getRegisterIndex()))
// this virtualRegister was used in this instruction and is also defined. We need to move
// this virtual register to its alias first and then save it to memory.
{
emitter.emitStoreAfter(*instruction.getPrimitive(), &instruction.getLinks(),
vReg.getAlias(), *vReg.equivalentRegister[vrcStackSlot]);
defPtr->getVirtualRegisterPtr().initialize(vReg.getAlias());
}
else
{
emitter.emitStoreAfter(*instruction.getPrimitive(), &instruction.getLinks(),
vReg, *vReg.equivalentRegister[vrcStackSlot]);
}
}
}
}
while (!grNeedLoad.empty())
{
PRUint32 nl = grNeedLoad.get();
VirtualRegister& nlReg = vRegManager.getVirtualRegister(nl);
Instruction& lastUse = *nlReg.spillInfo.lastUsingInstruction;
emitter.emitLoadAfter(*lastUse.getPrimitive(), lastUse.getLinks().prev,
nlReg.getAlias(), *nlReg.equivalentRegister[vrcStackSlot]);
nlReg.releaseSelf();
}
while (!fpNeedLoad.empty())
{
PRUint32 nl = fpNeedLoad.get();
VirtualRegister& nlReg = vRegManager.getVirtualRegister(nl);
Instruction& lastUse = *nlReg.spillInfo.lastUsingInstruction;
emitter.emitLoadAfter(*lastUse.getPrimitive(), lastUse.getLinks().prev,
nlReg.getAlias(), *nlReg.equivalentRegister[vrcStackSlot]);
nlReg.releaseSelf();
}
// if(node.dfsNum == 8) printf("\n________End Node %d________\n", node.dfsNum);
}
}
#endif

View File

@@ -1,269 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _SPILLING_H_
#define _SPILLING_H_
#include "Fundamentals.h"
#include <string.h>
#include "RegisterAllocator.h"
#include "RegisterAllocatorTools.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Instruction.h"
#include "SparseSet.h"
template <class RegisterPressure>
class Spilling
{
private:
static void insertStoreAfter(Instruction& instruction, RegisterName name);
static void insertLoadBefore(Instruction& instruction, RegisterName name);
public:
static void calculateSpillCosts(RegisterAllocator& registerAllocator);
static void insertSpillCode(RegisterAllocator& registerAllocator);
};
struct SpillCost
{
double loads;
double stores;
double copies;
double cost;
bool infinite;
};
template <class RegisterPressure>
void Spilling<RegisterPressure>::insertSpillCode(RegisterAllocator& registerAllocator)
{
Uint32 rangeCount = registerAllocator.rangeCount;
RegisterName* name2range = registerAllocator.name2range;
Pool& pool = registerAllocator.pool;
SparseSet currentLive(pool, rangeCount);
SparseSet needLoad(pool, rangeCount);
SparseSet mustSpill(pool, rangeCount);
SparseSet& willSpill = *registerAllocator.willSpill;
ControlGraph& controlGraph = registerAllocator.controlGraph;
RegisterPressure::Set* liveOut = registerAllocator.liveness.liveOut;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
for (Uint32 n = 0; n < nNodes; n++) {
needLoad.clear();
currentLive = liveOut[n];
mustSpill = currentLive;
InstructionList& instructions = nodes[n]->getInstructions();
for (InstructionList::iterator i = instructions.end(); !instructions.done(i);) {
Instruction& instruction = instructions.get(i);
i = instructions.retreat(i);
InstructionUse* useBegin = instruction.getInstructionUseBegin();
InstructionUse* useEnd = instruction.getInstructionUseEnd();
InstructionUse* usePtr;
InstructionDefine* defineBegin = instruction.getInstructionDefineBegin();
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
InstructionDefine* definePtr;
bool foundLiveDefine = false;
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
if (currentLive.test(name2range[definePtr->getRegisterName()])) {
foundLiveDefine = true;
break;
}
} else {
foundLiveDefine = true;
break;
}
if (defineBegin != defineEnd && !foundLiveDefine) {
fprintf(stderr, "!!! Removed instruction because it was only defining unused registers !!!\n");
instruction.remove();
}
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
RegisterName range = name2range[definePtr->getRegisterName()];
#ifdef DEBUG
if (needLoad.test(range))
if (!mustSpill.test(range) && registerAllocator.spillCost[range].infinite && willSpill.test(range)) {
fprintf(stderr, "Tried to spill a register with infinite spill cost\n");
abort();
}
#endif // DEBUG
if (willSpill.test(range))
insertStoreAfter(instruction, range);
needLoad.clear(range);
}
if (instruction.getFlags() & ifCopy)
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName range = name2range[usePtr->getRegisterName()];
if (!currentLive.test(range))
for (SparseSet::iterator r = needLoad.begin(); !needLoad.done(r); r = needLoad.advance(r)) {
RegisterName load = RegisterName(needLoad.get(r));
if (willSpill.test(load))
insertLoadBefore(instruction, load);
mustSpill.set(load);
}
needLoad.clear();
}
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
currentLive.clear(name2range[definePtr->getRegisterName()]);
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName range = name2range[usePtr->getRegisterName()];
currentLive.set(range);
needLoad.set(range);
}
}
for (SparseSet::iterator l = needLoad.begin(); !needLoad.done(l); l = needLoad.advance(l)) {
RegisterName load = RegisterName(needLoad.get(l));
if (willSpill.test(load))
insertLoadBefore(instructions.first(), load);
}
}
}
template <class RegisterPressure>
void Spilling<RegisterPressure>::insertLoadBefore(Instruction& /*instruction*/, RegisterName name)
{
fprintf(stdout, "will insert load for range %d\n", name);
}
template <class RegisterPressure>
void Spilling<RegisterPressure>::insertStoreAfter(Instruction& /*instruction*/, RegisterName name)
{
fprintf(stdout, "will insert store for range %d\n", name);
}
template <class RegisterPressure>
void Spilling<RegisterPressure>::calculateSpillCosts(RegisterAllocator& registerAllocator)
{
Uint32 rangeCount = registerAllocator.rangeCount;
RegisterName* name2range = registerAllocator.name2range;
Pool& pool = registerAllocator.pool;
SparseSet live(pool, rangeCount);
SparseSet needLoad(pool, rangeCount);
SparseSet mustSpill(pool, rangeCount);
SparseSet alreadyStored(pool, rangeCount); // FIX: should get this from previous spilling.
SpillCost* cost = new SpillCost[rangeCount];
memset(cost, '\0', rangeCount * sizeof(SpillCost));
ControlGraph& controlGraph = registerAllocator.controlGraph;
RegisterPressure::Set* liveOut = registerAllocator.liveness.liveOut;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
for (Uint32 n = 0; n < nNodes; n++) {
ControlNode& node = *nodes[n];
double weight = doLog10(node.loopDepth);
needLoad.clear();
live = liveOut[n];
mustSpill = live;
InstructionList& instructions = nodes[n]->getInstructions();
for (InstructionList::iterator i = instructions.end(); !instructions.done(i); i = instructions.retreat(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useBegin = instruction.getInstructionUseBegin();
InstructionUse* useEnd = instruction.getInstructionUseEnd();
InstructionUse* usePtr;
InstructionDefine* defineBegin = instruction.getInstructionDefineBegin();
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
InstructionDefine* definePtr;
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister()) {
RegisterName range = name2range[definePtr->getRegisterName()];
if (needLoad.test(range))
if (!mustSpill.test(range))
cost[range].infinite = true;
if ((false /* !rematerializable(range) */ || !needLoad.test(range)) && !alreadyStored.test(range))
cost[range].stores += weight;
needLoad.clear(range);
}
if (instruction.getFlags() & ifCopy)
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
if (!live.test(name2range[usePtr->getRegisterName()])) {
for (SparseSet::iterator l = needLoad.begin(); !needLoad.done(l); l = needLoad.advance(l)) {
Uint32 range = needLoad.get(l);
cost[range].loads += weight;
mustSpill.set(range);
}
needLoad.clear();
}
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
live.clear(name2range[definePtr->getRegisterName()]);
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName range = name2range[usePtr->getRegisterName()];
live.set(range);
needLoad.set(range);
}
if (instruction.getFlags() & ifCopy) {
assert(useBegin != useEnd && useBegin[0].isRegister());
assert(defineBegin != defineEnd && defineBegin[0].isRegister());
RegisterName source = name2range[useBegin[0].getRegisterName()];
RegisterName destination = name2range[defineBegin[0].getRegisterName()];
cost[source].copies += weight;
cost[destination].copies += weight;
}
}
for (SparseSet::iterator s = needLoad.begin(); !needLoad.done(s); s = needLoad.advance(s))
cost[needLoad.get(s)].loads += weight;
}
for (Uint32 r = 0; r < rangeCount; r++) {
SpillCost& c = cost[r];
c.cost = 2 * (c.loads + c.stores) - c.copies;
}
registerAllocator.spillCost = cost;
}
#endif // _SPILLING_H_

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@@ -1,239 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _SPLITS_H_
#define _SPLITS_H_
#include "Fundamentals.h"
#include <string.h>
#include "Pool.h"
#include "ControlGraph.h"
#include "ControlNodes.h"
#include "Instruction.h"
#include "RegisterAllocator.h"
#include "RegisterAllocatorTools.h"
UT_EXTERN_LOG_MODULE(RegAlloc);
template <class RegisterPressure>
struct Splits
{
static void calculateSplitCosts(RegisterAllocator& registerAllocator);
static bool findSplit(RegisterAllocator& registerAllocator, RegisterName* color, RegisterName range);
static void insertSplitCode(RegisterAllocator& registerAllocator);
};
struct SplitCost
{
double loads;
double stores;
};
template <class RegisterPressure>
void Splits<RegisterPressure>::insertSplitCode(RegisterAllocator& /*registerAllocator*/)
{
// FIX
}
template <class RegisterPressure>
bool Splits<RegisterPressure>::findSplit(RegisterAllocator& registerAllocator, RegisterName* color, RegisterName range)
{
Pool& pool = registerAllocator.pool;
NameLinkedList** neighborsWithColor = new(pool) NameLinkedList*[6]; // FIX
memset(neighborsWithColor, '\0', 6 * sizeof(NameLinkedList*));
InterferenceGraph<RegisterPressure>& iGraph = registerAllocator.iGraph;
for (InterferenceVector* vector = iGraph.getInterferenceVector(range); vector != NULL; vector = vector->next)
for (Int32 i = vector->count - 1; i >=0; --i) {
RegisterName neighbor = vector->neighbors[i];
RegisterName c = color[neighbor];
if (c < 6) { // FIX
NameLinkedList* node = new(pool) NameLinkedList();
node->name = neighbor;
node->next = neighborsWithColor[c];
neighborsWithColor[c] = node;
}
}
bool splitAroundName = true;
LiveRangeGraph<RegisterPressure>& lGraph = registerAllocator.lGraph;
RegisterName bestColor = RegisterName(6); // FIX
double bestCost = registerAllocator.spillCost[range].cost;
SplitCost* splitCost = registerAllocator.splitCost;
for (RegisterName i = RegisterName(0); i < 6; i = RegisterName(i + 1)) { // FIX
double splitAroundNameCost = 0.0;
bool canSplitAroundName = true;
SplitCost& sCost = splitCost[range];
double addedCost = 2.0 * (sCost.stores + sCost.loads);
for (NameLinkedList* node = neighborsWithColor[i]; node != NULL; node = node->next) {
RegisterName neighbor = node->name;
if (lGraph.haveEdge(neighbor, range)) {
canSplitAroundName = false;
break;
} else
splitAroundNameCost += addedCost;
}
if (canSplitAroundName && splitAroundNameCost < bestCost) {
bestCost = splitAroundNameCost;
bestColor = i;
splitAroundName = true;
}
double splitAroundColorCost = 0.0;
bool canSplitAroundColor = true;
for (NameLinkedList* node = neighborsWithColor[i]; node != NULL; node = node->next) {
RegisterName neighbor = node->name;
if (lGraph.haveEdge(range, neighbor)) {
canSplitAroundColor = false;
break;
} else {
SplitCost& sCost = splitCost[neighbor];
double addedCost = 2.0 * (sCost.stores + sCost.loads);
splitAroundColorCost += addedCost;
}
}
if (canSplitAroundColor && splitAroundColorCost < bestCost) {
bestCost = splitAroundColorCost;
bestColor = i;
splitAroundName = false;
}
}
if (bestColor < RegisterName(6)) {
color[range] = bestColor;
registerAllocator.splitFound = true;
NameLinkedList** splitAround = registerAllocator.splitAround;
if (splitAroundName)
for (NameLinkedList* node = neighborsWithColor[bestColor]; node != NULL; node = node->next) {
NameLinkedList* newNode = new(pool) NameLinkedList();
newNode->name = node->name;
newNode->next = splitAround[range];
splitAround[range] = newNode;
}
else
for (NameLinkedList* node = neighborsWithColor[bestColor]; node != NULL; node = node->next) {
NameLinkedList* newNode = new(pool) NameLinkedList();
RegisterName neighbor = node->name;
newNode->name = range;
newNode->next = splitAround[neighbor];
splitAround[neighbor] = newNode;
}
trespass("Found a split");
return true;
}
return false;
}
template <class RegisterPressure>
void Splits<RegisterPressure>::calculateSplitCosts(RegisterAllocator& registerAllocator)
{
Pool& pool = registerAllocator.pool;
Uint32 rangeCount = registerAllocator.rangeCount;
RegisterName* name2range = registerAllocator.name2range;
SplitCost* splitCost = new(pool) SplitCost[rangeCount];
memset(splitCost, '\0', rangeCount * sizeof(SplitCost));
SparseSet live(pool, rangeCount);
RegisterPressure::Set* liveIn = registerAllocator.liveness.liveIn;
RegisterPressure::Set* liveOut = registerAllocator.liveness.liveOut;
ControlGraph& controlGraph = registerAllocator.controlGraph;
ControlNode** nodes = controlGraph.dfsList;
Uint32 nNodes = controlGraph.nNodes;
for (Uint32 n = 0; n < nNodes; n++) {
ControlNode& node = *nodes[n];
double weight = doLog10(node.loopDepth);
live = liveOut[n];
ControlEdge* successorsEnd = node.getSuccessorsEnd();
for (ControlEdge* successorsPtr = node.getSuccessorsBegin(); successorsPtr < successorsEnd; successorsPtr++) {
ControlNode& successor = successorsPtr->getTarget();
if (successor.getControlKind() != ckEnd) {
RegisterPressure::Set& successorLiveIn = liveIn[successor.dfsNum];
for (SparseSet::iterator i = live.begin(); !live.done(i); i = live.advance(i)) {
RegisterName name = RegisterName(live.get(i));
if (!successorLiveIn.test(name))
splitCost[name].loads += doLog10(successor.loopDepth);
}
}
}
InstructionList& instructions = node.getInstructions();
for (InstructionList::iterator i = instructions.end(); !instructions.done(i); i = instructions.retreat(i)) {
Instruction& instruction = instructions.get(i);
InstructionUse* useBegin = instruction.getInstructionUseBegin();
InstructionUse* useEnd = instruction.getInstructionUseEnd();
InstructionUse* usePtr;
InstructionDefine* defineBegin = instruction.getInstructionDefineBegin();
InstructionDefine* defineEnd = instruction.getInstructionDefineEnd();
InstructionDefine* definePtr;
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
splitCost[name2range[definePtr->getRegisterName()]].stores += weight;
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister()) {
RegisterName range = name2range[usePtr->getRegisterName()];
if (!live.test(range)) {
if (&instruction != &instructions.last())
splitCost[range].loads += weight;
else {
ControlEdge* successorsEnd = node.getSuccessorsEnd();
for (ControlEdge* successorsPtr = node.getSuccessorsBegin(); successorsPtr < successorsEnd; successorsPtr++)
splitCost[range].loads += doLog10(successorsPtr->getTarget().loopDepth);
}
}
}
for (definePtr = defineBegin; definePtr < defineEnd; definePtr++)
if (definePtr->isRegister())
live.clear(name2range[definePtr->getRegisterName()]);
for (usePtr = useBegin; usePtr < useEnd; usePtr++)
if (usePtr->isRegister())
live.set(name2range[usePtr->getRegisterName()]);
}
}
NameLinkedList** splitAround = new(pool) NameLinkedList*[rangeCount];
memset(splitAround, '\0', rangeCount * sizeof(NameLinkedList*));
registerAllocator.splitAround = splitAround;
registerAllocator.splitCost = splitCost;
registerAllocator.splitFound = false;
}
#endif // _SPLITS_H_

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@@ -1,186 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#include "Fundamentals.h"
#include "HashTable.h"
#include "Timer.h"
#include "Pool.h"
static Pool pool; // Pool for the Timer class.
static HashTable<TimerEntry*> timerEntries(pool); // Timers hashtable.
const nTimersInABlock = 128; // Number of timers in a block.
static PRTime *timers = new(pool) PRTime[nTimersInABlock]; // A block of timers.
static Uint8 nextTimer = 0; // nextAvailableTimer.
//
// Calibrate the call to PR_Now().
//
static PRTime calibrate()
{
PRTime t = PR_Now();
PRTime& a = *new(pool) PRTime();
// Call 10 times the PR_Now() function.
a = PR_Now(); a = PR_Now(); a = PR_Now(); a = PR_Now(); a = PR_Now(); a = PR_Now();
a = PR_Now(); a = PR_Now(); a = PR_Now(); a = PR_Now(); a = PR_Now(); a = PR_Now();
t = (PR_Now() - t + 9) / 10;
return t;
}
static PRTime adjust = calibrate();
//
// Return the named timer..
//
TimerEntry& Timer::getTimerEntry(const char* name)
{
if (!timerEntries.exists(name)) {
TimerEntry* newEntry = new(pool) TimerEntry();
newEntry->accumulator = 0;
newEntry->running = false;
timerEntries.add(name, newEntry);
}
return *timerEntries[name];
}
//
// Return a reference to a new timer.
//
PRTime& Timer::getNewTimer()
{
if (nextTimer >= nTimersInABlock) {
timers = new(pool) PRTime[nTimersInABlock];
nextTimer = 0;
}
return timers[nextTimer++];
}
static Uint32 timersAreFrozen = 0;
//
// Start the named timer.
//
void Timer::start(const char* name)
{
if (timersAreFrozen)
return;
freezeTimers();
TimerEntry& timer = getTimerEntry(name);
PR_ASSERT(!timer.running);
timer.accumulator = 0;
timer.running = true;
timer.done = false;
unfreezeTimers();
}
//
// Stop the named timer.
//
void Timer::stop(const char* name)
{
if (timersAreFrozen)
return;
freezeTimers();
TimerEntry& timer = getTimerEntry(name);
PR_ASSERT(timer.running);
timer.running = false;
timer.done = true;
unfreezeTimers();
}
//
// Freeze all the running timers.
//
void Timer::freezeTimers()
{
PRTime when = PR_Now() - adjust;
if (timersAreFrozen == 0) {
Vector<TimerEntry*> entries = timerEntries;
Uint32 count = entries.size();
for (Uint32 i = 0; i < count; i++) {
TimerEntry& entry = *entries[i];
if (entry.running) {
entry.accumulator += (when - *entry.startTime);
}
}
}
timersAreFrozen++;
}
//
// Unfreeze all the running timers.
//
void Timer::unfreezeTimers()
{
PR_ASSERT(timersAreFrozen != 0);
timersAreFrozen--;
if (timersAreFrozen == 0) {
Vector<TimerEntry *> entries = timerEntries;
Uint32 count = entries.size();
PRTime& newStart = getNewTimer();
for (Uint32 i = 0; i < count; i++) {
TimerEntry& entry = *entries[i];
if (entry.running) {
entry.startTime = &newStart;
}
}
newStart = PR_Now();
}
}
//
// Print the named timer in the file f.
//
void Timer::print(FILE* f, const char *name)
{
if (timersAreFrozen)
return;
freezeTimers();
TimerEntry& timer = getTimerEntry(name);
PR_ASSERT(timer.done);
PRTime elapsed = timer.accumulator;
if (elapsed >> 32) {
fprintf(f, "[timer %s out of range]\n", name);
} else {
fprintf(f, "[%dus in %s]\n", Uint32(elapsed), name);
}
fflush(f);
unfreezeTimers();
}

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@@ -1,80 +0,0 @@
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _TIMER_H_
#define _TIMER_H_
#include "Fundamentals.h"
#include "HashTable.h"
#include "prtime.h"
//
// Naming convention:
// As the class Timer contains only static methods, the timer's name should start with the
// module name. Otherwise starting 2 timers with the same name will assert.
//
#ifndef NO_TIMER
struct TimerEntry
{
PRTime *startTime; // Current time when we start the timer.
PRTime accumulator; // Time spent in this timer.
bool running; // True if the timer is running.
bool done; // True if the timer was running and was stopped.
};
class Timer
{
private:
// Return the named timer.
static TimerEntry& getTimerEntry(const char* name);
// Return a reference to a new Timer.
static PRTime& getNewTimer();
public:
// Start the timer.
static void start(const char* name);
// Stop the timer.
static void stop(const char* name);
// Freeze all the running timers.
static void freezeTimers();
// Unfreeze all the running timers.
static void unfreezeTimers();
// Print the timer.
static void print(FILE* f, const char *name);
};
inline void startTimer(const char* name) {Timer::start(name);}
inline void stopTimer(const char* name) {Timer::stop(name); Timer::print(stdout, name);}
#define START_TIMER_SAFE Timer::freezeTimers();
#define END_TIMER_SAFE Timer::unfreezeTimers();
#define TIMER_SAFE(x) START_TIMER_SAFE x; END_TIMER_SAFE
#else /* NO_TIMER */
inline void startTimer(const char* /*name*/) {}
inline void stopTimer(const char* /*name*/) {}
#define START_TIMER_SAFE
#define END_TIMER_SAFE
#define TIMER_SAFE(x) x;
#endif /* NO_TIMER */
#endif /* _TIMER_H_ */

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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*
* The contents of this file are subject to the Netscape Public License
* Version 1.0 (the "NPL"); you may not use this file except in
* compliance with the NPL. You may obtain a copy of the NPL at
* http://www.mozilla.org/NPL/
*
* Software distributed under the NPL is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
* for the specific language governing rights and limitations under the
* NPL.
*
* The Initial Developer of this code under the NPL is Netscape
* Communications Corporation. Portions created by Netscape are
* Copyright (C) 1998 Netscape Communications Corporation. All Rights
* Reserved.
*/
#ifndef _VIRTUAL_REGISTER_H_
#define _VIRTUAL_REGISTER_H_
#include "Fundamentals.h"
#include "IndexedPool.h"
#include <string.h>
#include "RegisterTypes.h"
#include "RegisterClass.h"
//------------------------------------------------------------------------------
// VirtualRegister - 24b
class Instruction;
class VirtualRegister : public IndexedObject<VirtualRegister>
{
public:
Instruction* definingInstruction; // Instruction defining this VR.
// Initialize a VR of the given classKind.
VirtualRegister(RegisterClassKind /*classKind*/) : definingInstruction(NULL) {}
// Return the defining instruction for this VR.
Instruction* getDefiningInstruction() const {return definingInstruction;}
// Set the defining instruction.
void setDefiningInstruction(Instruction& insn);
};
// Return true if the VirtualRegisters are equals. The only way 2 VRs can be equal is if
// they have the same index. If they have the same index then they are at the same
// address in the indexed pool.
//
inline bool operator == (const VirtualRegister& regA, const VirtualRegister& regB) {return &regA == &regB;}
//------------------------------------------------------------------------------
// VirtualRegisterManager -
struct PreColoredRegister
{
RegisterID id;
RegisterName color;
};
class VirtualRegisterManager
{
private:
IndexedPool<VirtualRegister> registerPool;
PreColoredRegister machineRegister[6];
public:
VirtualRegisterManager()
{
for (Uint32 i = 0; i < 6; i++)
machineRegister[i].id = invalidID;
}
// Return the VirtualRegister at the given index.
VirtualRegister& getVirtualRegister(RegisterName name) const {return registerPool.get(name);}
// Return a new VirtualRegister.
RegisterID newVirtualRegister(RegisterClassKind classKind)
{
VirtualRegister& vReg = *new(registerPool) VirtualRegister(classKind);
RegisterID rid;
setName(rid, RegisterName(vReg.getIndex()));
setClass(rid, classKind);
return rid;
}
RegisterID newMachineRegister(RegisterName name, RegisterClassKind classKind)
{
RegisterID rid = machineRegister[name].id;
if (rid == invalidID) {
rid = newVirtualRegister(classKind);
DEBUG_ONLY(setMachineRegister(rid));
machineRegister[name].id = rid;
machineRegister[name].color = name;
}
return rid;
}
PreColoredRegister* getMachineRegistersBegin() const {return (PreColoredRegister*) machineRegister;} // FIX
PreColoredRegister* getMachineRegistersEnd() const {return (PreColoredRegister*) &machineRegister[6];} // FIX
// Return the VirtualRegister universe size.
Uint32 getSize() {return registerPool.getSize();}
void setSize(Uint32 size) {registerPool.setSize(size);}
};
#endif // _VIRTUAL_REGISTER_H_

452
mozilla/js/ref/ChangeLog Normal file
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Tag JSREF_RELEASE_19980414 (4/14/98):
- RegExp unicode fix.
- Added new iterator-style JSObjectOps enumeration API for host objects.
See jspubtd.h for details.
Tag JSREF_RELEASE_19980413 (4/13/98):
- Date fixes:
- ECMAv1 fix: fixed function length for Date setters.
- Bug workaround: avoid MSVC optimizer bug in Date.
- Y2K fix: Use the verbose '%#c' date formatter for toLocaleString
on windows, to get a 4 digit date.
- New thread safety fixes from bjorn:
- Added more asserts to catch cases where the thread
identifier stored in the context is out of synch with the current
thread. JS_ATOMIC_ADDREF now calls a function instead of a
macro, so that when compare-and-swap is implemented using busy-wait
(e.g. SPARC v8), we avoid being confused by the busy value. For the same
reason, we now call AtomicRead at certain places in jslock.c. Finally, the
environment variable JS_NO_THIN_LOCKS, when set, effectively turns off
the thin locks so that all locking is done using NSPR only.
- ECMAv1 numeric fixes: print preceding 0 when formatting 0.4, ignore supplied
radix to Number.prototype.toString when printing non-finite numbers.
Tag JSREF_RELEASE_19980403 (4/3/98):
- API renaming: JS_NewRuntime for JS_Init, JS_DestroyRuntime for JS_Finish
(the old names are maintained for backward binary compatibility; the new
names are macros).
- Improved JS_THREADSAFE locking, with compare-and-swap based optimization of
the uncontested lock and unlock cases to avoid DLL-crossing and worse native
OS locking overhead.
The Request/GC interlock enforced by JS_BeginRequest, JS_EndRequest, JS_GC,
and JS_MaybeGC allows requests on the same cx to nest (JS_BeginRequest may
be called more than once before JS_EndRequest, so long as the number of End
calls matches the number of Begin calls).
Thread-safety for prarena.c and prdtoa.c, based on jslock.h/JS_THREADSAFE.
- Experimental JS exception implementation, subject to change. Any value may
be thrown. The catch expression must be of the form (v) or (var v). Catch
code must re-throw as there is no way yet for the compiler to decide that no
catch clause matched (and more than one catch clause makes no sense, yet --
no finally yet, either).
- JS_ConvertArguments API addition, for converting an argc/argv pair according
to a simplified scanf-like format string.
- JS_GetPropertyAttributes and JS_SetPropertyAttributes API additions, which
take C-string property names (Unicode string and indexed elements TBD).
- JS_CloneFunctionObject, for server-like environments where code (functions)
should be shared in a prototype object, but data (global variables) must be
per request in a set of objects, one per concurrent request. You load the
functions in the prototype, then "fault them in" on demand via the request
object's resolve hook, using JS_CloneFunctionObject to make a lightweight
copy that has the right scope (__parent__) link.
- Whacked js.c (more whacking needed) so it uses fewer secret js_* calls and
more JS PUBLIC/FRIEND API entry points.
- Simplified Windows MSDEV build regime to use js.mak/mdp only, which builds
the DLL as a sub-project, then compiles js.c and links the JS shell.
- Fix a lying comment about JS_AddRoot in README (which is being turned into a
real "JS API tutorial" document, due soon).
- Better error reporting for an operand that does not convert to function, and
spiffed up the decompiler (jsopcode.c) to remove hardwired opcode lengths.
- Atom indexing does not abuse the atom's next link and a flags bit, which had
been done in haste long ago (and not fixed till now), but which required that
compilation be single-threaded throughout a runtime.
- ECMAv2 change: undefined is a top-level property with undefined value (it may
be overwritten or deleted by a script).
- ECMAv1 fix: arguments is implemented as a separate object from Call, but with
Netscape extensions (callee, caller).
- ECMAv1 fix: array length and indexes are uint32.
- ECMAv1 fixes enabled by major overhaul of the compiler to generate a tree of
parse-node structures and generate code from it. The bugs had to do with the
order of evaluation and conversion in for/in loop and assignment expressions.
This change also moved the "quickening" for name-to-arg/var-slot bytecodes
from the interpreter to the compiler.
- Proposed ECMAv2 toSource method, which produces compilable object and array
initializers and new expressions to reconstruct a given graph.
- Proposed ECMAv2 instanceof operator, based on hasInstance JSObjectOp and
(for maximum code-sharing among native object classes, with one exception)
JSClass methods. There is also js_IsDelegate, for checking whether a given
object is a prototype of another.
- To-be-proposed ECMAv2 in operator, inspired by for/in loop syntax: ('p' in o)
for o = {p:1} is true; (1 in o) for o[1] defined (even with value undefined)
is true. Note distinction between typeof o.p == "undefined" and ('p' in o).
- XDR (eXternal Data Representation) code to support Script.prototype.freeze
and Script.thaw/Script.prototype.thaw. You can store a persistent, portable
encoding of a script (including its top-level functions and all their kids)
and load it later.
Exception "try-notes" are not currently XDR'd; this will be fixed next time.
- Recent GC bugs mentioned in snews://secnews.netscape.com/netscape.dev.jsref
have been fixed. The patches were posted already; this tarball rolls them
up along with other fixes and improvements. We've had help from Netscape's
Application Products Division in stress-testing this release; we are pretty
confident that JS_THREADSAFE GC and request execution work well.
One new fix: finalizers are run without the GC lock held, to allow them to
call JS_RemoveRoot and otherwise to avoid AB-BA deadlocks.
- Call and construct are now optional methods in JSObjectOps and JSClass. The
hack of converting a regexp to a function is no longer necessary, and script
callability (shorthand for script.exec) uses the JSClass call hook likewise.
- Fixed standard class bootstrapping bug that left an extra Object instance
in the middle of the prototype chain for Date, RegExp, etc. (all but Object
and Function) instances.
- String.prototype.split ECMAv1 conformance restoration (split-by-empty-string
was stupidly broken last time).
Tag JSREF_RELEASE_19980219 (2/16/98):
- Fixed very recent i++ (for undefined i) crash-bug (also prior, longstanding
bug where i++ for undefined i resulted in NaN).
- ECMA conformance for [[DefaultValue]] (8.6.2.6), ToBoolean (9.2), and null
(default) this-parameter handling (10.2.3).
- New bytecodes paving the way for ECMA-conformant for/in loops and unqualified
name assignment.
- JS1.2 String.prototype.replace did not emulate Perl4's expansion of $` to be
the global left context (not from last local match). Essentially the same
bug bit replace for the empty-string global match case, which "bumps along"
by one character, but failed to include that character in local left context
(so "abc".replace(/ */g, 'X') produced "XXXX" instead of "XaXbXcX").
- Fix recent regression that clamped String.prototype.split's limit argument at
the subject string's length.
- Fixed type mismatch problems in #if !JS_HAS_REGEXPS code.
Tag JSREF_RELEASE_19980216 (2/16/98):
- Fixed stuck GC lock by adding JS_UNLOCK_GC at the bottom of js_GC.
Tag JSREF_RELEASE_19980213 (2/13/98):
- Add JS_ShutDown API, which must be called after all JSRuntimes have been
destroyed by JS_Finish calls, and from a single thread, when shutting down
or restarting the program in which JSRef is embedded. This is needed to
avoid leaking the deflated_string_cache and (JS_THREADSAFE only) lock.
Tag JSREF_RELEASE_19980212 (2/12/98):
- Finer-grained locking. Instead of one big, reentrant lock around the entire
runtime, there are distinct locks:
- The non-reentrant runtime lock, a binary semaphore to protect the runtime's
contextList and other members.
- An atom state lock used only in jsatom.c for a thread-safe internal atom
table API. This lock is never held while calling out from jsatom.c to
other modules that may acquire locks, and no caller into jsatom.c's lock-
acquiring entry points does so while holding a lock of its own (the GC
calls non-locking entry points only).
- A lock and pair of condition variables for interlocking GC execution with
script execution. The GC may run only when no script requests are running,
or when at most one is running and it has invoked the GC from its branch
callback. The new JS_SetGCCallback API may be used to supply a function to
be called at the beginning and end of GC -- if called at the beginning, a
false return value will cancel the GC run.
- A reentrant lock per native object map (scope) to protect the JSScope and
its parts (JSProperty, JSSymbol, and PRHashTable structures) as well as the
slots vectors of all instances sharing the scope (the prototype object and
any unmutated clones of it).
The model jslock.c and jslock.h provided include four new header files that
are not yet supplied with JSRef:
- pratomic.h for PR_COMPARE_AND_SWAP_WORDS and PR_COMPARE_AND_SWAP_INT32
macros that take an address, an old value, and a new value, and return true
if the old value is at the address, in which case the new value is atomicly
stored there; and return false without changing memory otherwise.
- prcvar.h for the PRCondVar condition variable type and its operations (New,
Destroy, Wait, Notify, and NotifyAll).
- prlock.h for the PRLock binary semaphore type and its operations (New,
Destroy, Lock, and Unlock).
More lock overhead and lock-free synchronization optimizations are coming in
a future JSRef release. In anticipation of these changes, the JS_THREADSAFE
version of JS_GetClass now requires an initial JSContext *cx argument along
with JSObject *obj.
- New String.prototype.replace feature: a function expression may be passed
as the second argument, in which case it will be invoked with the match and
parenthesized submatch strings as arguments, followed by input and index
(these are come from the extended array returned by RegExp.prototype.exec and
String.prototype.match).
This "lambda replacement" approximates Perl's s///e flag; the idea came from
Mike Shaver (shaver@netscape.com). Here's a example function that replaces
any number with an F after it (for Fahrenheit) with its Celsius conversion:
// f2c("32F, 212F, or 0F") => "0C, 100C, or -17.77777777777778C"
function f2c(x) {
var s = String(x)
return s.replace(/(\d+(\.\d*)?)F\b/g,
function ($0,$1,$2) { return (($1-32) * 5/9) + "C" })
}
- First-character discrimination optimization for regular expressions, plus a
fix to anchor-search for \b and \B.
- A first-class Script object to decompose eval into its compile and exec parts
(so you can compile outside a long loop, then exec in the loop body to avoid
recompiling invariant source). See jsscript.c.
- More ECMA fixes:
- bitwise logical and shift operators use the correct ECMA type conversions,
intermediate types, and boundary behavior.
- Array.prototype.push emulates Perl5 for JS versions other than 1.2; there
it emulated Perl4, except when no arguments were passed (it would return
the array object bound to this in that case; fixed to return undefined).
- All generic Array methods now update a length property, in case no such
property existed in the object that delegates to Array.prototype, or that
refers to the particular method.
- Except for JS1.2, Array.prototype.splice always returns an array, even when
given no arguments or a zero-length slice. JS1.2 compatibility continues.
- NaN Date fixes.
- JSFunctionSpec's nargs member now species the "best arity" of the function,
which ECMA specifies as the value of the function's length property. So to
allocate local GC roots, use the new extra member of JSFunctionSpec and let
nargs count only the minimum or optimum number of desired arguments.
- Relational and equality operator fixes too gnarly and subtle to describe
here, affecting mainly the hint argument (or lack of it) to valueOf.
- A new JS_IsConstructing API and underlying support, so ECMA [[Call]] and
[[Construct]] can be distinguished.
- A JS_InitClass extension to tolerate NULL for the constructor native C
function argument -- this causes a class like Math to be created, where
the class object is not callable or constructable.
- Fixes to handle non-finite indexes in several string and array methods.
- A high-level object operation dispatch table has been added. See JSObjectOps
in jsapi.h, and the new flags and function pointers in JSClass. To provide a
table of object operations, your class should set the JSCLASS_HAS_OBJECTOPS
flag and implement the getObjectOps class method, returning the address of a
static or otherwise appropriate-lifetime JSObjectOps structure. The methods
in this struct will be specified in a forthcoming version of the JS API doc.
The JSCLASS_NEW_ENUMERATE flag can be used without adding getObjectOps to
your class, to say that its enumerate method returns a JSIdArray containing
all lazy and eager property ids for an object, instead of having to define
all lazily-bound properties in the object, to minimize locking and reduce
the space cost of old-style enumerate.
- Atoms are now garbage-collected. To clarify the fact that symbol table ids
are either tagged jsval-like integers, or else JSAtom pointers, a new typedef
called jsid (equivalent to jsval in C) has been introduced.
- Major changes to remove JSProperty's object member, in order to optimize for
space. These mostly entail an extra &obj2 or &pobj result parameter being
passed to js_FindProperty, js_LookupProperty, etc., to capture the prototype
or original object in which the property was found.
- Updated Windows MSDEV makefiles to support MSDEV5.0 as well as 4.2:
- js32.mak, an NMAKE makefile, builds js32.dll
- jsshell.mak, an NMAKE makefile, now recursively invokes js32.mak to build
js32.dll
- jsshelld.mak and jsshelld.mdp, collectively a 4.2 IDE project, build
jsshell.exe and have a subproject that builds js32.dll. These two project
files are not derived from the other .mak files, nor are the other .mak
files derived from them.
- JS_PUBLIC_API etc. macros in jspubtd.h, used by jsapi.h and a few other .h
files, to optimize linkage within the Windows DLL.
Tag JSREF_RELEASE_19971128 (11/28/97):
- Major Unicode changes. JSString has a jschar *chars member now, not
char *bytes; it points to a counted array of uint16 (jschar) elements.
The scanner handles \uXXXX escapes; so does the regular expression parser.
JS_GetStringBytes(str) now returns the ISO-Latin-1 counterpart of str's
Unicode sequence by decimating into separate memory whose lifetime matches
that of str->chars. The API entry points taking char *name or char *base
arguments now have UC counterparts (except for the JS_*Property entries)
that take jschar *name, size_t length or similar argument-pairs. There is
a new JS_ValueToUint16 API entry for converting from a jsval to a Unicode
code point.
- The beginnings of JavaScript 1.3 version support, including === and !== for
equality by type and value identity, and sharp variables (see below).
- Linux support from Mike Shaver (shaver@ingenia.ca, shaver@netscape.com) in
config/Linux_All.mk. OS/2 ifdefs from IBM (initials DSR?), via Dan Libby
(danda@netscape.com).
- A new gc command in the js shell for testing, useful in conjunction with
the GC_MARK_DEBUG ifdef'd code in jsgc.c and js.c to plug leaks and find
stuck references. Use the new API entry point JS_AddNamedRoot in preference
to JS_AddRoot, which still exists but provides no debugging name for the GC
thing graph root that it establishes. See also JS_DumpNamedRoots.
- JSCLASS_NEW_RESOLVE flag and JSNewResolveOp function pointer typedef, for
more efficient unbound name resolution.
- Sharp variables (based on Common Lisp's dispatching macros of the same form)
for expressing cycles and join-points in object graphs created by object and
array initializers. For example,
#1={p:#2={q:42}, r:{cycle:#1#, joinPoint:#2#}}
creates an object, call it o, where o.p and o.r.joinPoint both reach the same
object, which has a property named q with value 42; and o.r.cycle is o.
In a future release, the final JS1.3 version will return object and array
initializer strings from {Object,Array}.prototype.toSource methods, rather
than toString, for ECMA and backward compatibility.
- More ECMA conformance fixes, apart from Unicode:
- New ECMA-conformant jsdate.c by Mike McCabe (mccabe@netscape.com).
- Improved equality and relational operator implementations.
- Correct division operator result sign.
- The unary-plus operator.
- NaN and Infinity top-level properties.
- Setting a read-only property fails silently, rather than stopping the
script with an error report.
- Deleting a permanent property fails with a false return from the delete
operator. If the property is not in the object addressed in the delete
expression, or it is successfully deleted, the expression results in true.
- The beginnings of finer-grained, non-nesting/low-level locking in jslock.h,
used in jsstr.c for the deflated_string_cache_lock. For this version, you
need to provide a PRLock typedef and PR_NewLock, PR_DestroyLock, PR_Lock,
and PR_Unlock functions that implement a binary semaphore.
- Performance improvements based on aggressive, coherent use of the property
cache (part of the JSRuntime structure). This required a fix to restore a
watchpoint associated with a deleted property when a new property with the
same identifier is created in the same object.
- Regular expression bugfixes and Unicode extensions in jsregexp.c and jsstr.c.
- Fixed Perl bug where \xZ or similar was translated to "\0Z".
- Fixed another Perl bug where [x-\d] matched {'x', '-', '0', ... '9'} but
[\d-x] matched only the digits. The second is now equivalent to the first.
- Fixed JS bug where only $1 through $9 could be used in the replacement
string passed to String.prototype.replace. Also allow literal $ in the
replacement string if it is preceded by \ (as a JS literal: "\\$").
- Fixed non-JS1.2 versions to return left context from start of global match
instead of from end of last local match (Perl4 had a similar bug which 1.2
emulated too much). This alters "$`" expansion in replacement strings.
Tag JSREF_1_14_RELEASE (around 7/22/97):
- JSTaskState and related API entry point names have been renamed to use the
trendier "Runtime" rather than "TaskState", ditto rt or runtime for task.
- JS_GetScriptPrincipals is no longer in jsapi.h, it moved to jsdbgapi.h and
has a new interface that takes the JSScript * being queried. It therefore
requires JS_FrameIterator and JS_GetFrameScript.
- JS_LockGCThing/JS_UnlockGCThing and their macro wrappers JSVAL_LOCK/UNLOCK
are deprecated as of now. Use JS_AddRoot to register a pointer to the thing
you would lock, and clear the pointer and/or JS_RemoveRoot its address later
to unlock the thing. I would like to remove GC thing-locking in a future
release; it precludes too many alternative GC implementations.
- ECMA conformant Date API, including get/setFullYear and the UTC variants
to all the get/set methods.
- ECMA conformant Number.MIN_VALUE, which is the smallest denorm now, not
the smallest normal as in all past JS versions.
- ECMA comformant isFinite() function.
- ECMA signed 0 and NaN number to string conversions.
- Watcom (__WATCOMC__) support for PC builds.
Quick update (4/27/97):
- Prototypes are no longer constructed in JS_InitClass. If you want a class
prototype to be constructed by the native 'constructor' function passed to
JS_InitClass, you can save JS_InitClass's return value and do it yourself:
proto = JS_InitClass(...);
ok = JS_CallFunctionName(cx, proto, "constructor", argc, argc, &rval);
- Object, array, and function literals are supported on input for JS_VERSION
1.2 at compile-time. Only for JS_SetVersion(cx, JSVERSION_1_2) at runtime:
object.toString() returns an object literal, likewise for array.toString,
and function.toString returns an anonymous function literall (rather than
the definition of a function named "anonymous") for functions created using
new Function(...).
- Final RegExp API: regexp.exec and string.match always return null on mismatch
(not -1), and always return a match array on match (whether parens matched or
not). The match array's 0'th element is the matching string, and any paren
submatches are in elements 1..N. The index and input properties can be used
to find left and right context without resort to the RegExp.leftContext and
RegExp.rightContext statics:
leftContext = match.input.substring(0, match.input.index)
rightContext = match.input.substring(match.input.index + match[0].length)
- A JS_MaybeGC entry point in the API, safe to use from branch callbacks (well
tested) and arbitrary preemption points (not so well tested) when garbage may
be piling up, but a forced GC (JS_GC) is not desirable.
- Various bugfixes and improvements.
Newer news (3/18/97):
- Regular expressions a la Perl are supported.
- Perl array methods push, pop, shift, unshift, and splice are supported.
- Perl substr, with its righteous interpretation of negative offset, is also
now supported.
- Lexical closures a la Scheme are supported. See ycomb.js.
- Property caching and other performance improvements have been added.
- Mac CodeWarrior JSRef.prj and MacPrefix.h files are now bundled.
- Windows MSDEV4.2 .mak and .mdp files bundled.
- The 32-bit Windows version of prcpucfg.h is shipped; on Unix platforms, you
should remove this file or set it aside and let gmake generate the right one
for your host architecture.
- Classes whose objects have private data (JS_SetPrivate/JS_GetPrivate) must
flag that fact with the JSCLASS_HAS_PRIVATE flag in their JSClass structs.
- There are also two new property ops in JSClass, addProperty and delProperty.
News flashes (12/31/96):
- Define JS_THREADSAFE and write code in jslock.c for multi-threaded JS.
- NOTE: JS_EvaluateScript and JS_ExecuteScript no longer return a JSVAL_LOCKed
result in *rval -- this was never safe in a multithreaded environment, when
*rval referred to an object tree of depth > 1, because a preempting GC run
could reclaim the unrooted, descendent objects. Instead, callers of these
API entry points must use JS_AddRoot and JS_RemoveRoot to maintain the rval
pointer argument in the GC's root set. See JS_AddRoot comments below.
- Labeled statements and break and continue to label a la Java are supported.
- The switch statement is now supported. You can switch on any primitive type
value (number, string, boolean).
- Numerous performance enhancements, notably the quick ops at the bottom of
jsopcode.def, have been made.

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PFR0TEfiJ8Q9cEh9bBf@NfJ:

View File

@@ -0,0 +1,2 @@
#define XP_MAC 1
#define JSFILE 1

299
mozilla/js/ref/Makefile Normal file
View File

@@ -0,0 +1,299 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# JSRef GNUmake makefile.
#
# Set os+release dependent make variables
OS_ARCH := $(subst /,_,$(shell uname -s))
# Attempt to differentiate between SunOS 5.4 and x86 5.4
OS_CPUARCH := $(shell uname -m)
ifeq ($(OS_CPUARCH),i86pc)
OS_RELEASE := $(shell uname -r)_$(OS_CPUARCH)
else
OS_RELEASE := $(shell uname -r)
endif
# Virtually all Linux versions are identical.
# Any distinctions are handled in linux.h
ifeq ($(OS_ARCH),Linux)
OS_CONFIG := Linux_All
else
OS_CONFIG := $(OS_ARCH)$(OS_OBJTYPE)$(OS_RELEASE)
endif
ASFLAGS =
DEFINES =
include config/$(OS_CONFIG).mk
ifdef BUILD_OPT
OPTIMIZER += -O
DEFINES += -UDEBUG -DNDEBUG -UDEBUG_$(shell whoami)
OBJDIR_TAG = _OPT
else
ifdef USE_MSVC
OPTIMIZER = -Zi
else
OPTIMIZER = -g
endif
DEFINES += -DDEBUG -DDEBUG_$(shell whoami)
OBJDIR_TAG = _DBG
endif
#DEFINES += -DJS_THREADSAFE
ifdef JS_NO_THIN_LOCKS
DEFINES += -DJS_USE_ONLY_NSPR_LOCKS
endif
# Name of the binary code directories
OBJDIR = $(OS_CONFIG)$(OBJDIR_TAG).OBJ
VPATH = $(OBJDIR)
# Automatic make dependencies file
DEPENDENCIES = $(OBJDIR)/.md
define MAKE_OBJDIR
if test ! -d $(@D); then rm -rf $(@D); mkdir $(@D); fi
endef
# Look in OBJDIR to find prcpucfg.h
INCLUDES = -I$(OBJDIR)
#
# XCFLAGS may be set in the environment or on the gmake command line
#
CFLAGS = $(OPTIMIZER) $(OS_CFLAGS) $(DEFINES) $(INCLUDES) \
-DJSFILE $(XCFLAGS)
LDFLAGS = -lm $(XLDFLAGS) -Lfdlibm -lfdm
# For purify
PURE_CFLAGS = -DXP_UNIX $(OPTIMIZER) $(PURE_OS_CFLAGS) $(DEFINES) \
$(INCLUDES) $(XCFLAGS)
#
# JS file lists
#
PR_HFILES = \
prarena.h \
prassert.h \
prclist.h \
prdtoa.h \
prhash.h \
prlong.h \
prmacos.h \
prosdep.h \
prpcos.h \
prprintf.h \
prtime.h \
prtypes.h \
prunixos.h \
$(NULL)
JS_HFILES = \
jsarray.h \
jsatom.h \
jsbool.h \
jsconfig.h \
jscntxt.h \
jsdate.h \
jsemit.h \
jsfun.h \
jsgc.h \
jsinterp.h \
jslock.h \
jsmath.h \
jsnum.h \
jsobj.h \
jsopcode.h \
jsparse.h \
jsprvtd.h \
jspubtd.h \
jsregexp.h \
jsscan.h \
jsscope.h \
jsscript.h \
jsstr.h \
jsxdrapi.h \
$(NULL)
API_HFILES = \
jsapi.h \
jsdbgapi.h \
$(NULL)
HFILES = $(PR_HFILES) $(JS_HFILES) $(API_HFILES)
PR_CFILES = \
prarena.c \
prassert.c \
prdtoa.c \
prhash.c \
prlog2.c \
prlong.c \
prprintf.c \
prtime.c \
$(NULL)
JS_CFILES = \
jsapi.c \
jsarray.c \
jsatom.c \
jsbool.c \
jscntxt.c \
jsdate.c \
jsdbgapi.c \
jsemit.c \
jsfun.c \
jsgc.c \
jsinterp.c \
jslock.c \
jsmath.c \
jsnum.c \
jsobj.c \
jsopcode.c \
jsparse.c \
jsregexp.c \
jsscan.c \
jsscope.c \
jsscript.c \
jsstr.c \
jsxdrapi.c \
$(NULL)
LIB_CFILES = $(PR_CFILES) $(JS_CFILES)
LIB_ASFILES := $(wildcard *_$(OS_ARCH).s)
PROG_CFILES = js.c
ifdef USE_MSVC
LIB_OBJS = $(addprefix $(OBJDIR)/, $(LIB_CFILES:.c=.obj))
PROG_OBJS = $(addprefix $(OBJDIR)/, $(PROG_CFILES:.c=.obj))
else
LIB_OBJS = $(addprefix $(OBJDIR)/, $(LIB_CFILES:.c=.o))
LIB_OBJS += $(addprefix $(OBJDIR)/, $(LIB_ASFILES:.s=.o))
PROG_OBJS = $(addprefix $(OBJDIR)/, $(PROG_CFILES:.c=.o))
endif
CFILES = $(LIB_CFILES) $(PROG_CFILES)
OBJS = $(LIB_OBJS) $(PROG_OBJS)
ifdef USE_MSVC
LIBRARY = $(OBJDIR)/js32.dll
PROGRAM = $(OBJDIR)/js
else
LIBRARY = $(OBJDIR)/libjs.a
PROGRAM = $(OBJDIR)/js
endif
ifdef USE_MSVC
TARGETS = $(LIBRARY) # $(PROGRAM) not supported for MSVC yet
else
TARGETS = fdlibm/libfdm.a $(LIBRARY) $(PROGRAM)
endif
all: $(TARGETS)
clean:
rm -rf $(OBJS)
cd fdlibm; gmake clean
clobber:
rm -rf $(OBJS) $(TARGETS) $(DEPENDENCIES)
cd fdlibm; gmake clean
depend:
gcc -MM $(CFLAGS) $(JS_CFILES)
fdlibm/libfdm.a:
cd fdlibm; gmake
$(OBJDIR)/%: %.c
@$(MAKE_OBJDIR)
$(CC) -o $@ $(CFLAGS) $*.c $(LDFLAGS)
$(OBJDIR)/%.o: %.c
@$(MAKE_OBJDIR)
$(CC) -o $@ -c $(CFLAGS) $*.c
$(OBJDIR)/%.o: %.s
@$(MAKE_OBJDIR)
$(AS) -o $@ $(ASFLAGS) $*.s
# windows only
$(OBJDIR)/%.obj: %.c
@$(MAKE_OBJDIR)
$(CC) -Fo$(OBJDIR)/ -c $(CFLAGS) $*.c
ifeq ($(OS_ARCH),OS2)
$(LIBRARY): $(LIB_OBJS)
$(AR) $@ $? $(AR_OS2_SUFFIX)
$(RANLIB) $@
else
ifdef USE_MSVC
$(LIBRARY): $(LIB_OBJS)
link.exe $(LIB_LINK_FLAGS) /base:0x61000000 \
/out:"$@" /pdb:"$(OBJDIR)/js32.pdb" /implib:"$(OBJDIR)/js32.lib" $?
else
$(LIBRARY): $(LIB_OBJS)
$(AR) rv $@ $?
$(RANLIB) $@
endif
endif
#NSPR_LIBRARY = ../../dist/$(OBJDIR)/lib/libnspr21.so
NSPR_LIBRARY =
$(PROGRAM): $(PROG_OBJS) $(LIBRARY)
$(CC) -o $@ $(CFLAGS) $(PROG_OBJS) $(LIBRARY) $(NSPR_LIBRARY) $(LDFLAGS)
$(PROGRAM).pure: $(PROG_OBJS) $(LIBRARY)
purify $(PUREFLAGS) \
$(CC) -o $@ $(PURE_OS_CFLAGS) $(PROG_OBJS) $(LIBRARY) $(LDFLAGS)
$(HFILES) $(CFILES): $(OBJDIR)/prcpucfg.h
ifdef PREBUILT_CPUCFG
$(OBJDIR)/prcpucfg.h: prcpucfg.h
cp prcpucfg.h $(OBJDIR)
else
$(OBJDIR)/prcpucfg.h: $(OBJDIR)/prcpucfg
rm -f $@
$(OBJDIR)/prcpucfg > $@
$(OBJDIR)/prcpucfg: $(OBJDIR)/prcpucfg.o
$(CC) -o $@ $(OBJDIR)/prcpucfg.o
endif
#
# Hardwire dependencies on jsopcode.def
#
jsopcode.h jsopcode.c: jsopcode.def
-include $(DEPENDENCIES)
TARNAME = jsref.tar
TARFILES = files `cat files`
tar:
tar cvf $(TARNAME) $(TARFILES)
gzip $(TARNAME)
SUFFIXES: .i
%.i: %.c
$(CC) -C -E $(CFLAGS) $< > $*.i

674
mozilla/js/ref/README Normal file
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@@ -0,0 +1,674 @@
This is the README file for the JavaScript Reference (JSRef) implementation.
It consists of build conventions and instructions, source code conventions, a
design walk-through, and a brief file-by-file description of the source.
JSRef builds a library or DLL containing the JavaScript runtime (compiler,
interpreter, decompiler, garbage collector, atom manager, standard classes).
It then compiles a small "shell" program and links that with the library to
make an interpreter that can be used interactively and with test .js files to
run scripts.
The current version of JSRef lacks a conformance testsuite. We aim to provide
one as soon as possible.
Quick start tip: skip to "Using the JS API" below, build js, and play with the
object named "it" (start by setting 'it.noisy = true').
Brendan Eich, 9/17/96
------------------------------------------------------------------------------
Build conventions:
- On Windows, use MSDEV4.2 (js*.mdp) or 5.0 (js*.mak).
- On Mac, use CodeWarrior 1.x (JSRef.prj.hqx) or 2 (JSRef.prj2.hqx).
- On Unix, use vendor cc or gcc (ftp://prep.ai.mit.edu/pub/gnu) for compiling,
and use gmake for building.
To compile optimized code, pass BUILD_OPT=1 on the nmake/gmake command line
or preset it in the environment or makefile. The C preprocessor macro DEBUG
will be undefined, and NDEBUG (archaic Unix-ism for "No Debugging") will be
defined. Without BUILD_OPT, DEBUG is predefined and NDEBUG is undefined.
On Unix, your own debug flag, DEBUG_$USER, will be defined or undefined as
BUILD_OPT is unset or set.
(Linux autoconf support way overdue; coming some day soon, I promise.)
- To add C compiler options from the make command line, set XCFLAGS=-Dfoo.
To predefine -D or -U options in the makefile, set DEFINES.
To predefine -I options in the makefile, set INCLUDES.
- To turn on GC instrumentation, define JS_GCMETER.
- To enable multi-threaded execution, define JS_THREADSAFE and flesh out the
stubs and required headers in jslock.c/.h. See the JS API docs for more.
- To turn on the arena package's instrumentation, define PR_ARENAMETER.
- To turn on the hash table package's metering, define PR_HASHMETER.
Naming and coding conventions:
- Public function names begin with JS_ followed by capitalized "intercaps",
e.g. JS_NewObject.
- Extern but library-private function names use a js_ prefix and mixed case,
e.g. js_LookupSymbol.
- Most static function names have unprefixed, mixed-case names: GetChar.
- But static native methods of JS objects have lowercase, underscore-separated
or intercaps names, e.g., str_indexOf.
- And library-private and static data use underscores, not intercaps (but
library-private data do use a js_ prefix).
- Scalar type names are lowercase and js-prefixed: jsdouble.
- Aggregate type names are JS-prefixed and mixed-case: JSObject.
- Macros are generally ALL_CAPS and underscored, to call out potential
side effects, multiple uses of a formal argument, etc.
- Four spaces of indentation per statement nesting level.
- Tabs are taken to be eight spaces, and an Emacs magic comment at the top of
each file tries to help. If you're using MSVC or similar, you'll want to
set tab width to 8, or convert these files to be space-filled.
- DLL entry points have their return type expanded within a PR_PUBLIC_API()
macro call, to get the right Windows secret type qualifiers in the right
places for both 16- and 32-bit builds.
- Callback functions that might be called from a DLL are similarly macroized
with PR_STATIC_CALLBACK (if the function otherwise would be static to hide
its name) or PR_CALLBACK (this macro takes no type argument; it should be
used after the return type and before the function name).
Using the JS API:
- Starting up:
/*
* Tune this to avoid wasting space for shallow stacks, while saving on
* malloc overhead/fragmentation for deep or highly-variable stacks.
*/
#define STACK_CHUNK_SIZE 8192
JSRuntime *rt;
JSContext *cx;
/* You need a runtime and one or more contexts to do anything with JS. */
rt = JS_Init(1000000L);
if (!rt)
fail("can't create JavaScript runtime");
cx = JS_NewContext(rt, STACK_CHUNK_SIZE);
if (!cx)
fail("can't create JavaScript context");
/*
* The context definitely wants a global object, in order to have standard
* classes and functions like Date and parseInt. See below for details on
* JS_NewObject.
*/
JSObject *globalObj;
globalObj = JS_NewObject(cx, &my_global_class, 0, 0);
JS_InitStandardClasses(cx, globalObj);
- Defining objects and properties:
/* Statically initialize a class to make "one-off" objects. */
JSClass my_class = {
"MyClass",
/* All of these can be replaced with the corresponding JS_*Stub
function pointers. */
my_addProperty, my_delProperty, my_getProperty, my_setProperty,
my_enumerate, my_resolve, my_convert, my_finalize
};
JSObject *obj;
/*
* Define an object named in the global scope that can be enumerated by
* for/in loops. The parent object is passed as the second argument, as
* with all other API calls that take an object/name pair. The prototype
* passed in is null, so the default object prototype will be used.
*/
obj = JS_DefineObject(cx, globalObj, "myObject", &my_class, 0,
JSPROP_ENUMERATE);
/*
* Define a bunch of properties with a JSPropertySpec array statically
* initialized and terminated with a null-name entry. Besides its name,
* each property has a "tiny" identifier (MY_COLOR, e.g.) that can be used
* in switch statements (in a common my_getProperty function, for example).
*/
enum my_tinyid {
MY_COLOR, MY_HEIGHT, MY_WIDTH, MY_FUNNY, MY_ARRAY, MY_RDONLY
};
static JSPropertySpec my_props[] = {
{"color", MY_COLOR, JSPROP_ENUMERATE},
{"height", MY_HEIGHT, JSPROP_ENUMERATE},
{"width", MY_WIDTH, JSPROP_ENUMERATE},
{"funny", MY_FUNNY, JSPROP_ENUMERATE},
{"array", MY_ARRAY, JSPROP_ENUMERATE},
{"rdonly", MY_RDONLY, JSPROP_READONLY},
{0}
};
JS_DefineProperties(cx, obj, my_props);
/*
* Given the above definitions and call to JS_DefineProperties, obj will
* need this sort of "getter" method in its class (my_class, above). See
* the example for the "It" class in js.c.
*/
static JSBool
my_getProperty(JSContext *cx, JSObject *obj, jsval id, jsval *vp)
{
if (JSVAL_IS_INT(id)) {
switch (JSVAL_TO_INT(id)) {
case MY_COLOR: *vp = . . .; break;
case MY_HEIGHT: *vp = . . .; break;
case MY_WIDTH: *vp = . . .; break;
case MY_FUNNY: *vp = . . .; break;
case MY_ARRAY: *vp = . . .; break;
case MY_RDONLY: *vp = . . .; break;
}
}
return JS_TRUE;
}
- Defining functions:
/* Define a bunch of native functions first: */
static JSBool
my_abs(JSContext *cx, JSObject *obj, uintN argc, jsval *argv, jsval *rval)
{
jsdouble x, z;
if (!JS_ValueToNumber(cx, argv[0], &x))
return JS_FALSE;
z = (x < 0) ? -x : x;
return JS_NewDoubleValue(cx, z, rval);
}
. . .
/*
* Use a JSFunctionSpec array terminated with a null name to define a
* bunch of native functions.
*/
static JSFunctionSpec my_functions[] = {
/* name native nargs */
{"abs", my_abs, 1},
{"acos", my_acos, 1},
{"asin", my_asin, 1},
. . .
{0}
};
/*
* Pass a particular object to define methods for it alone. If you pass
* a prototype object, the methods will apply to all instances past and
* future of the prototype's class (see below for classes).
*/
JS_DefineFunctions(cx, globalObj, my_functions);
- Defining classes:
/*
* This pulls together the above API elements by defining a constructor
* function, a prototype object, and properties of the prototype and of
* the constructor, all with one API call.
*
* Initialize a class by defining its constructor function, prototype, and
* per-instance and per-class properties. The latter are called "static"
* below by analogy to Java. They are defined in the constructor object's
* scope, so that 'MyClass.myStaticProp' works along with 'new MyClass()'.
*
* JS_InitClass takes a lot of arguments, but you can pass null for any of
* the last four if there are no such properties or methods.
*
* Note that you do not need to call JS_InitClass to make a new instance of
* that class -- otherwise there would be a chicken-and-egg problem making
* the global object -- but you should call JS_InitClass if you require a
* constructor function for script authors to call via new, and/or a class
* prototype object ('MyClass.prototype') for authors to extend with new
* properties at run-time.
*/
protoObj = JS_InitClass(cx, globalObj, &my_class,
/* native constructor function and min arg count */
MyClass, 0,
/* prototype object properties and methods -- these
will be "inherited" by all instances through
delegation up the instance's prototype link. */
my_props, my_methods,
/* class constructor properties and methods */
my_static_props, my_static_methods);
- Running scripts:
/* These should indicate source location for diagnostics. */
char *filename;
uintN lineno;
/*
* The return value comes back here -- if it could be a GC thing, you must
* add it to the GC's "root set" with JS_AddRoot(cx, &thing) where thing
* is a JSString *, JSObject *, or jsdouble *, and remove the root before
* rval goes out of scope, or when rval is no longer needed.
*/
jsval rval;
JSBool ok;
/*
* Some example source in a C string. Larger, non-null-terminated buffers
* can be used, if you pass the buffer length to JS_EvaluateScript.
*/
char *source = "x * f(y)";
ok = JS_EvaluateScript(cx, globalObj, source, strlen(source),
filename, lineno, &rval);
if (ok) {
/* Should get a number back from the example source. */
jsdouble d;
ok = JS_ValueToNumber(cx, rval, &d);
. . .
}
- Calling functions:
/* Call a global function named "foo" that takes no arguments. */
ok = JS_CallFunctionName(cx, globalObj, "foo", 0, 0, &rval);
jsval argv[2];
/* Call a function in obj's scope named "method", passing two arguments. */
argv[0] = . . .;
argv[1] = . . .;
ok = JS_CallFunctionName(cx, obj, "method", 2, argv, &rval);
- Shutting down:
/* For each context you've created: */
JS_DestroyContext(cx);
/* And finally: */
JS_Finish(rt);
- Debugging API
See the trap, untrap, watch, unwatch, line2pc, and pc2line commands in js.c.
Also the (scant) comments in jsdbgapi.h.
Design walk-through:
This section must be brief for now -- it could easily turn into a book.
- JS "JavaScript Proper"
JS modules declare and implement the JavaScript compiler, interpreter,
decompiler, GC and atom manager, and standard classes.
JavaScript uses untyped bytecode and runtime type tagging of data values.
The jsval type is a signed machine word that contains either a signed integer
value (if the low bit is set), or a type-tagged pointer or boolean value (if
the low bit is clear). Tagged pointers all refer to 8-byte-aligned things in
the GC heap.
Objects consist of a possibly shared structural description, called the map
or scope; and unshared property values in a vector, called the slots. Object
properties are associated with nonnegative integers stored in jsvals, or with
atoms (unique string descriptors) if named by an identifier or a non-integral
index expression.
Scripts contain bytecode, source annotations, and a pool of string, number,
and identifier literals. Functions are objects that extend scripts or native
functions with formal parameters, a literal syntax, and a distinct primitive
type ("function").
The compiler consists of a recursive-descent parser and a random-logic rather
than table-driven lexical scanner. Semantic and lexical feedback are used to
disambiguate hard cases such as missing semicolons, assignable expressions
("lvalues" in C parlance), etc. The parser generates bytecode as it parses,
using fixup lists for downward branches and code buffering and rewriting for
exceptional cases such as for loops. It attempts no error recovery.
The interpreter executes the bytecode of top-level scripts, and calls itself
indirectly to interpret function bodies (which are also scripts). All state
associated with an interpreter instance is passed through formal parameters
to the interpreter entry point; most implicit state is collected in a type
named JSContext. Therefore, all API and almost all other functions in JSRef
take a JSContext pointer as their first argument.
The decompiler translates postfix bytecode into infix source by consulting a
separate byte-sized code, called source notes, to disambiguate bytecodes that
result from more than one grammatical production.
The GC is a mark-and-sweep, non-conservative (perfect) collector. It can
allocate only fixed-sized things -- the current size is two machine words.
It is used to hold JS object and string descriptors (but not property lists
or string bytes), and double-precision floating point numbers. It runs
automatically only when maxbytes (as passed to JS_Init) bytes of GC things
have been allocated and another thing-allocation request is made. JS API
users should call JS_GC or JS_MaybeGC between script executions or from the
branch callback, as often as necessary.
An important point about the GC's "perfection": you must add roots for new
objects created by your native methods if you store references to them into
a non-JS structure in the malloc heap or in static data. Also, if you make
a new object in a native method, but do not store it through the rval result
parameter (see math_abs in the "Using the JS API" section above) so that it
is in a known root, the object is guaranteed to survive only until another
new object is created. Either lock the first new object when making two in
a row, or store it in a root you've added, or store it via rval.
The atom manager consists of a hash table associating strings uniquely with
scanner/parser information such as keyword type, index in script or function
literal pool, etc. Atoms play three roles in JSRef: as literals referred to
by unaligned 16-bit immediate bytecode operands, as unique string descriptors
for efficient property name hashing, and as members of the root GC set for
perfect GC. This design therefore requires atoms to be manually reference
counted, from script literal pools (JSAtomMap) and object symbol (JSSymbol)
entry keys.
Native objects and methods for arrays, booleans, dates, functions, numbers,
and strings are implemented using the JS API and certain internal interfaces
used as "fast paths".
In general, errors are signaled by false or unoverloaded-null return values,
and are reported using JS_ReportError or one of its variants by the lowest
level in order to provide the most detail. Client code can substitute its
own error reporting function and suppress errors, or reflect them into Java
or some other runtime system as exceptions, GUI dialogs, etc.
- PR "Portable Runtime"
PR modules declare and implement fundamental representation types and macros,
arenas, hash tables, 64-bit integers, double-precision floating point to
string and back conversions, and date/time functions that are used by the JS
modules. The PR code is independent of JavaScript and can be used without
linking with the JS code.
In general, errors are signaled by false or unoverloaded-null return values,
but are not reported. Therefore, JS calls to PR functions check returns and
report errors as specifically as possible.
File walk-through:
- jsapi.c, jsapi.h
The public API to be used by almost all client code.
If your client code can't make do with jsapi.h, and must reach into a friend
or private js* file, please let us know so we can extend jsapi.h to include
what you need in a fashion that we can support over the long run.
- jspubtd.h, jsprvtd.h
These files exist to group struct and scalar typedefs so they can be used
everywhere without dragging in struct definitions from N different files.
The jspubtd.h file contains public typedefs, and is included by jsapi.h.
The jsprvtd.h file contains private typedefs and is included by various .h
files that need type names, but not type sizes or declarations.
- jsdbgapi.c, jsdbgapi.h
The Debugging API, still very much under development. Provided so far:
- Traps, with which breakpoints, single-stepping, step over, step out, and
so on can be implemented. The debugger will have to consult jsopcode.def
on its own to figure out where to plant trap instructions to implement
functions like step out, but a future jsdbgapi.h will provide convenience
interfaces to do these things.
At most one trap per bytecode can be set. When a script (JSScript) is
destroyed, all traps set in its bytecode are cleared.
- Watchpoints, for intercepting set operations on properties and running a
debugger-supplied function that receives the old value and a pointer to
the new one, which it can use to modify the new value being set.
- Line number to PC and back mapping functions. The line-to-PC direction
"rounds" toward the next bytecode generated from a line greater than or
equal to the input line, and may return the PC of a for-loop update part,
if given the line number of the loop body's closing brace. Any line after
the last one in a script or function maps to a PC one byte beyond the last
bytecode in the script.
An example, from perfect.js:
14 function perfect(n)
15 {
16 print("The perfect numbers up to " + n + " are:");
17
18 // We build sumOfDivisors[i] to hold a string expression for
19 // the sum of the divisors of i, excluding i itself.
20 var sumOfDivisors = new ExprArray(n+1,1);
21 for (var divisor = 2; divisor <= n; divisor++) {
22 for (var j = divisor + divisor; j <= n; j += divisor) {
23 sumOfDivisors[j] += " + " + divisor;
24 }
25 // At this point everything up to 'divisor' has its sumOfDivisors
26 // expression calculated, so we can determine whether it's perfect
27 // already by evaluating.
28 if (eval(sumOfDivisors[divisor]) == divisor) {
29 print("" + divisor + " = " + sumOfDivisors[divisor]);
30 }
31 }
32 delete sumOfDivisors;
33 print("That's all.");
34 }
The line number to PC and back mappings can be tested using the js program
with the following script:
load("perfect.js")
print(perfect)
dis(perfect)
print()
for (var ln = 0; ln <= 40; ln++) {
var pc = line2pc(perfect,ln)
var ln2 = pc2line(perfect,pc)
print("\tline " + ln + " => pc " + pc + " => line " + ln2)
}
The result of the for loop over lines 0 to 40 inclusive is:
line 0 => pc 0 => line 16
line 1 => pc 0 => line 16
line 2 => pc 0 => line 16
line 3 => pc 0 => line 16
line 4 => pc 0 => line 16
line 5 => pc 0 => line 16
line 6 => pc 0 => line 16
line 7 => pc 0 => line 16
line 8 => pc 0 => line 16
line 9 => pc 0 => line 16
line 10 => pc 0 => line 16
line 11 => pc 0 => line 16
line 12 => pc 0 => line 16
line 13 => pc 0 => line 16
line 14 => pc 0 => line 16
line 15 => pc 0 => line 16
line 16 => pc 0 => line 16
line 17 => pc 19 => line 20
line 18 => pc 19 => line 20
line 19 => pc 19 => line 20
line 20 => pc 19 => line 20
line 21 => pc 36 => line 21
line 22 => pc 53 => line 22
line 23 => pc 74 => line 23
line 24 => pc 92 => line 22
line 25 => pc 106 => line 28
line 26 => pc 106 => line 28
line 27 => pc 106 => line 28
line 28 => pc 106 => line 28
line 29 => pc 127 => line 29
line 30 => pc 154 => line 21
line 31 => pc 154 => line 21
line 32 => pc 161 => line 32
line 33 => pc 172 => line 33
line 34 => pc 172 => line 33
line 35 => pc 172 => line 33
line 36 => pc 172 => line 33
line 37 => pc 172 => line 33
line 38 => pc 172 => line 33
line 39 => pc 172 => line 33
line 40 => pc 172 => line 33
- jsconfig.h
Various configuration macros defined as 0 or 1 depending on how JS_VERSION
is defined (as 10 for JavaScript 1.0, 11 for JavaScript 1.1, etc.). Not all
macros are tested around related code yet. In particular, JS 1.0 support is
missing from JSRef. JS 1.2 support will appear in a future JSRef release.
- js.c
The "JS shell", a simple interpreter program that uses the JS API and more
than a few internal interfaces (some of these internal interfaces could be
replaced by jsapi.h calls). The js program built from this source provides
a test vehicle for evaluating scripts and calling functions, trying out new
debugger primitives, etc.
- jsarray.c, jsarray.h
- jsbool.c, jsbool.h
- jsdate.c, jsdate.h
- jsfun.c, jsfun.h
- jsmath.c, jsmath.h
- jsnum.c, jsnum.h
- jsstr.c, jsstr.h
These file pairs implement the standard classes and (where they exist) their
underlying primitive types. They have similar structure, generally starting
with class definitions and continuing with internal constructors, finalizers,
and helper functions.
- jsobj.c, jsobj.h
- jsscope.c, jsscope.h
These two pairs declare and implement the JS object system. All of the
following happen here:
- creating objects by class and prototype, and finalizing objects;
- defining, looking up, getting, setting, and deleting properties;
- creating and destroying properties and binding names to them.
The details of an object map (scope) are mostly hidden in jsscope.[ch],
where scopes start out as linked lists of symbols, and grow after some
threshold into PR hash tables.
- jsatom.c, jsatom.h
The atom manager. Contains well-known string constants, their atoms, the
global atom hash table and related state, the js_Atomize() function that
turns a counted string of bytes into an atom, and literal pool (JSAtomMap)
methods.
- jsgc.c, jsgc.h
[TBD]
- jsinterp.c, jsinterp.h
- jscntxt.c, jscntxt.h
The bytecode interpreter, and related functions such as Call and AllocStack,
live in interp.c. The JSContext constructor and destructor are factored out
into jscntxt.c for minimal linking when the compiler part of JS is split from
the interpreter part into a separate program.
- jsemit.c, jsemit.h
- jsopcode.def, jsopcode.c, jsopcode.h
- jsparse.c, jsparse.h
- jsscan.c, jsscan.h
- jsscript.c, jsscript.h
Compiler and decompiler modules. The jsopcode.def file is a C preprocessor
source that defines almost everything there is to know about JS bytecodes.
See its major comment for how to use it. For now, a debugger will use it
and its dependents such as jsopcode.h directly, but over time we intend to
extend jsdbgapi.h to hide uninteresting details and provide conveniences.
The code generator is split across paragraphs of code in jsparse.c, and the
utility methods called on JSCodeGenerator appear in jsemit.c. Source notes
generated by jsparse.c and jsemit.c are used in jsscript.c to map line number
to program counter and back.
- prtypes.h, prlog2.c
Fundamental representation types and utility macros. This file alone among
all .h files in JSRef must be included first by .c files. It is not nested
in .h files, as other prerequisite .h files generally are, since it is also
a direct dependency of most .c files and would be over-included if nested in
addition to being directly included.
The one "not-quite-a-macro macro" is the PR_CeilingLog2 function in prlog2.c.
- prarena.c, prarena.h
Last-In-First-Out allocation macros that amortize malloc costs and allow for
en-masse freeing. See the paper mentioned in prarena.h's major comment.
- prassert.c, prassert.h
The PR_ASSERT macro is used throughout JSRef source as a proof device to make
invariants and preconditions clear to the reader, and to hold the line during
maintenance and evolution against regressions or violations of assumptions
that it would be too expensive to test unconditionally at run-time. Certain
assertions are followed by run-time tests that cope with assertion failure,
but only where I'm too smart or paranoid to believe the assertion will never
fail...
- prclist.h
Doubly-linked circular list struct and macros.
- prcpucfg.c
This standalone program generates prcpucfg.h, a header file containing bytes
per word and other constants that depend on CPU architecture and C compiler
type model. It tries to discover most of these constants by running its own
experiments on the build host, so if you are cross-compiling, beware.
- prdtoa.c, prdtoa.h
David Gay's portable double-precision floating point to string conversion
code, with Permission To Use notice included.
- prhash.c, prhash.h
Portable, extensible hash tables. These use multiplicative hash for strength
reduction over division hash, yet with very good key distribution over power
of two table sizes. Collisions resolve via chaining, so each entry burns a
malloc and can fragment the heap.
- prlong.c, prlong.h
64-bit integer emulation, and compatible macros that use C's long long type
where it exists (my last company mapped long long to a 128-bit type, but no
real architecture does 128-bit ints yet).
- prosdep.h, prmacos.h, prpcos.h, prunixos.h, os/*.h
A bunch of annoying OS dependencies rationalized into a few "feature-test"
macros such as HAVE_LONG_LONG.
- prprintf.c, prprintf.h
Portable, buffer-overrun-resistant sprintf and friends.
For no good reason save lack of time, the %e, %f, and %g formats cause your
system's native sprintf, rather than PR_dtoa, to be used. This bug doesn't
affect JSRef, because it uses its own PR_dtoa call in jsnum.c to convert
from double to string, but it's a bug that we'll fix later, and one you
should be aware of if you intend to use a PR_*printf function with your own
floating type arguments -- various vendor sprintf's mishandle NaN, +/-Inf,
and some even print normal floating values inaccurately.
- prtime.c, prtime.h
Time functions. These interfaces are named in a way that makes local vs.
universal time confusion likely. Caveat emptor, and we're working on it.
To make matters worse, Java (and therefore JavaScript) uses "local" time
numbers (offsets from the epoch) in its Date class.

9
mozilla/js/ref/TODO Normal file
View File

@@ -0,0 +1,9 @@
- scriptable in jsref
- exposed w/o java in js
- immutable scopes
- so can revive SCOPE_TABLE stuff
- fast-as-prop-cache inline scopes for native objects
so elim prop-cache
- views
- global vars in ssjs object model
- html object model

View File

@@ -0,0 +1,56 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for IRIX
#
CPU_ARCH = mips
GFX_ARCH = x
RANLIB = /bin/true
#NS_USE_GCC = 1
ifdef NS_USE_GCC
CC = gcc
CCC = g++
AS = $(CC) -x assembler-with-cpp
ODD_CFLAGS = -Wall -Wno-format
ifdef BUILD_OPT
OPTIMIZER = -O6
endif
else
ifeq ($(OS_RELEASE),6.2)
CC = cc -32 -DIRIX6_2
endif
ifeq ($(OS_RELEASE),6.3)
CC = cc -32 -DIRIX6_3
endif
CCC = CC
ODD_CFLAGS = -fullwarn -xansi
ifdef BUILD_OPT
OPTIMIZER += -Olimit 4000
endif
endif
# For purify
HAVE_PURIFY = 1
PURE_OS_CFLAGS = $(ODD_CFLAGS) -DXP_UNIX -DSVR4 -DSW_THREADS -DIRIX
OS_CFLAGS = $(PURE_OS_CFLAGS) -MDupdate $(DEPENDENCIES)
BSDECHO = echo
MKSHLIB = $(LD) -shared

View File

@@ -0,0 +1,20 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for IRIX5.3
#
include config/IRIX.mk

View File

@@ -0,0 +1,20 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for IRIX6.3
#
include config/IRIX.mk

View File

@@ -0,0 +1,33 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
# Config for all versions of Linux
CC = gcc -Wall -Wno-format
CCC = g++ -Wall -Wno-format
RANLIB = echo
#.c.o:
# $(CC) -c -MD $*.d $(CFLAGS) $<
CPU_ARCH = x86 # XXX fixme
GFX_ARCH = x
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -D_BSD_SOURCE -DPOSIX_SOURCE -DLINUX
OS_LIBS = -lm -lc
ASFLAGS += -x assembler-with-cpp

View File

@@ -0,0 +1,78 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for SunOS4.1
#
CC = gcc
CCC = g++
RANLIB = ranlib
#.c.o:
# $(CC) -c -MD $*.d $(CFLAGS) $<
CPU_ARCH = sparc
GFX_ARCH = x
# A pile of -D's to build xfe on sunos
MOZ_CFLAGS = -DSTRINGS_ALIGNED -DNO_REGEX -DNO_ISDIR -DUSE_RE_COMP \
-DNO_REGCOMP -DUSE_GETWD -DNO_MEMMOVE -DNO_ALLOCA \
-DBOGUS_MB_MAX -DNO_CONST
# Purify doesn't like -MDupdate
NOMD_OS_CFLAGS = -DXP_UNIX -Wall -Wno-format -DSW_THREADS -DSUNOS4 -DNEED_SYSCALL \
$(MOZ_CFLAGS)
OS_CFLAGS = $(NOMD_OS_CFLAGS) -MDupdate $(DEPENDENCIES)
OS_LIBS = -ldl -lm
MKSHLIB = $(LD) -L$(MOTIF)/lib
HAVE_PURIFY = 1
MOTIF = /home/motif/usr
MOTIFLIB = -L$(MOTIF)/lib -lXm
INCLUDES += -I/usr/X11R5/include -I$(MOTIF)/include
NOSUCHFILE = /solaris-rm-f-sucks
LOCALE_MAP = $(DEPTH)/cmd/xfe/intl/sunos.lm
EN_LOCALE = en_US
DE_LOCALE = de
FR_LOCALE = fr
JP_LOCALE = ja
SJIS_LOCALE = ja_JP.SJIS
KR_LOCALE = ko
CN_LOCALE = zh
TW_LOCALE = zh_TW
I2_LOCALE = i2
IT_LOCALE = it
SV_LOCALE = sv
ES_LOCALE = es
NL_LOCALE = nl
PT_LOCALE = pt
LOC_LIB_DIR = /usr/openwin/lib/locale
BSDECHO = echo
#
# These defines are for building unix plugins
#
BUILD_UNIX_PLUGINS = 1
DSO_LDOPTS =
DSO_LDFLAGS =

View File

@@ -0,0 +1,65 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for SunOS5.3
#
CC = gcc -Wall -Wno-format
CCC = g++ -Wall -Wno-format
#CC = /opt/SUNWspro/SC3.0.1/bin/cc
RANLIB = echo
#.c.o:
# $(CC) -c -MD $*.d $(CFLAGS) $<
CPU_ARCH = sparc
GFX_ARCH = x
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS
OS_LIBS = -lsocket -lnsl -ldl
ASFLAGS += -P -L -K PIC -D_ASM -D__STDC__=0
HAVE_PURIFY = 1
NOSUCHFILE = /solaris-rm-f-sucks
ifndef JS_NO_ULTRA
ULTRA_OPTIONS := -xarch=v8plus
ULTRA_OPTIONSD := -DULTRA_SPARC
else
ULTRA_OPTIONS := -xarch=v8
ULTRA_OPTIONSD :=
endif
ifeq ($(OS_CPUARCH),sun4u)
DEFINES += $(ULTRA_OPTIONSD)
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,$(ULTRA_OPTIONS),$(ULTRA_OPTIONSD)
else
ASFLAGS += $(ULTRA_OPTIONS) $(ULTRA_OPTIONSD)
endif
endif
ifeq ($(OS_CPUARCH),sun4m)
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,-xarch=v8
else
ASFLAGS += -xarch=v8
endif
endif

View File

@@ -0,0 +1,66 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for SunOS5.4
#
ifdef NS_USE_NATIVE
CC = cc
CCC = CC
else
CC = gcc -Wall -Wno-format
CCC = g++ -Wall -Wno-format
endif
RANLIB = echo
CPU_ARCH = sparc
GFX_ARCH = x
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -D__svr4 -DSOLARIS
OS_LIBS = -lsocket -lnsl -ldl
ASFLAGS += -P -L -K PIC -D_ASM -D__STDC__=0
HAVE_PURIFY = 1
NOSUCHFILE = /solaris-rm-f-sucks
ifndef JS_NO_ULTRA
ULTRA_OPTIONS := -xarch=v8plus
ULTRA_OPTIONSD := -DULTRA_SPARC
else
ULTRA_OPTIONS := -xarch=v8
ULTRA_OPTIONSD :=
endif
ifeq ($(OS_CPUARCH),sun4u)
DEFINES += $(ULTRA_OPTIONSD)
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,$(ULTRA_OPTIONS),$(ULTRA_OPTIONSD)
else
ASFLAGS += $(ULTRA_OPTIONS) $(ULTRA_OPTIONSD)
endif
endif
ifeq ($(OS_CPUARCH),sun4m)
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,-xarch=v8
else
ASFLAGS += -xarch=v8
endif
endif

View File

@@ -0,0 +1,65 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for SunOS5.5
#
AS = as
CC = gcc -Wall -Wno-format
CCC = g++ -Wall -Wno-format
#CC = /opt/SUNWspro/SC3.0.1/bin/cc
RANLIB = echo
#.c.o:
# $(CC) -c -MD $*.d $(CFLAGS) $<
CPU_ARCH = sparc
GFX_ARCH = x
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS -D_SVID_GETTOD
OS_LIBS = -lsocket -lnsl -ldl
ASFLAGS += -P -L -K PIC -D_ASM -D__STDC__=0
HAVE_PURIFY = 1
NOSUCHFILE = /solaris-rm-f-sucks
ifndef JS_NO_ULTRA
ULTRA_OPTIONS := -xarch=v8plus
ULTRA_OPTIONSD := -DULTRA_SPARC
else
ULTRA_OPTIONS := -xarch=v8
ULTRA_OPTIONSD :=
endif
ifeq ($(OS_CPUARCH),sun4u)
DEFINES += $(ULTRA_OPTIONSD)
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,$(ULTRA_OPTIONS),$(ULTRA_OPTIONSD)
else
ASFLAGS += $(ULTRA_OPTIONS) $(ULTRA_OPTIONSD)
endif
endif
ifeq ($(OS_CPUARCH),sun4m)
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,-xarch=v8
else
ASFLAGS += -xarch=v8
endif
endif

View File

@@ -0,0 +1,60 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
#
# Config stuff for SunOS5.5
#
AS = as
CC = gcc -Wall -Wno-format
CCC = g++ -Wall -Wno-format
#CC = /opt/SUNWspro/SC3.0.1/bin/cc
RANLIB = echo
#.c.o:
# $(CC) -c -MD $*.d $(CFLAGS) $<
CPU_ARCH = sparc
GFX_ARCH = x
OS_CFLAGS = -DXP_UNIX -DSVR4 -DSYSV -DSOLARIS -D_SVID_GETTOD
OS_LIBS = -lsocket -lnsl -ldl
ASFLAGS += -P -L -K PIC -D_ASM -D__STDC__=0
HAVE_PURIFY = 1
NOSUCHFILE = /solaris-rm-f-sucks
ifndef JS_NO_ULTRA
ULTRA_OPTIONS := -xarch=v8plus -DULTRA_SPARC
else
ULTRA_OPTIONS := -xarch=v8
endif
ifeq ($(OS_CPUARCH),sun4u)
ASFLAGS += $(ULTRA_OPTIONS)
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,$(ULTRA_OPTIONS)
endif
else
ifeq ($(OS_CPUARCH),sun4m)
ASFLAGS += -xarch=v8
ifeq ($(findstring gcc,$(CC)),gcc)
DEFINES += -Wa,-xarch=v8
endif
endif
endif

View File

@@ -0,0 +1,44 @@
#
# The contents of this file are subject to the Netscape Public License
# Version 1.0 (the "NPL"); you may not use this file except in
# compliance with the NPL. You may obtain a copy of the NPL at
# http://www.mozilla.org/NPL/
#
# Software distributed under the NPL is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the NPL
# for the specific language governing rights and limitations under the
# NPL.
#
# The Initial Developer of this code under the NPL is Netscape
# Communications Corporation. Portions created by Netscape are
# Copyright (C) 1998 Netscape Communications Corporation. All Rights
# Reserved.
# Config for Windows NT using MS Visual C++ (version?)
CC = cl
RANLIB = echo
#.c.o:
# $(CC) -c -MD $*.d $(CFLAGS) $<
CPU_ARCH = x86 # XXX fixme
GFX_ARCH = win32
OS_CFLAGS = -DXP_PC -DWIN32 -D_WINDOWS -D_WIN32
OS_LIBS = -lm -lc
PREBUILT_CPUCFG = 1
USE_MSVC = 1
LIB_LINK_FLAGS=kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib\
advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib oldnames.lib /nologo\
/subsystem:windows /dll /incremental:yes /debug\
/machine:I386
CAFEDIR = t:/cafe
JCLASSPATH = $(CAFEDIR)/Java/Lib/classes.zip
JAVAC = $(CAFEDIR)/Bin/sj.exe
JAVAH = $(CAFEDIR)/Java/Bin/javah.exe
JCFLAGS = -I$(CAFEDIR)/Java/Include -I$(CAFEDIR)/Java/Include/win32

View File

@@ -0,0 +1,110 @@
#
# @(#)Makefile 1.4 95/01/18
#
# ====================================================
# Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
#
# Developed at SunSoft, a Sun Microsystems, Inc. business.
# Permission to use, copy, modify, and distribute this
# software is freely granted, provided that this notice
# is preserved.
# ====================================================
#
#
#
# There are two options in making libm at fdlibm compile time:
# _IEEE_LIBM --- IEEE libm; smaller, and somewhat faster
# _MULTI_LIBM --- Support multi-standard at runtime by
# imposing wrapper functions defined in
# fdlibm.h:
# _IEEE_MODE -- IEEE
# _XOPEN_MODE -- X/OPEN
# _POSIX_MODE -- POSIX/ANSI
# _SVID3_MODE -- SVID
#
# Here is how to set up CFLAGS to create the desired libm at
# compile time:
#
# CFLAGS = -D_IEEE_LIBM ... IEEE libm (recommended)
# CFLAGS = -D_SVID3_MODE ... Multi-standard supported
# libm with SVID as the
# default standard
# CFLAGS = -D_XOPEN_MODE ... Multi-standard supported
# libm with XOPEN as the
# default standard
# CFLAGS = -D_POSIX_MODE ... Multi-standard supported
# libm with POSIX as the
# default standard
# CFLAGS = ... Multi-standard supported
# libm with IEEE as the
# default standard
#
# NOTE: if scalb's second arguement is an int, then one must
# define _SCALB_INT in CFLAGS. The default prototype of scalb
# is double scalb(double, double)
#
#
# Default IEEE libm
#
CFLAGS = -D_IEEE_LIBM
CC = gcc
INCFILES = fdlibm.h
.INIT: $(INCFILES)
.KEEP_STATE:
src = k_standard.c k_rem_pio2.c \
k_cos.c k_sin.c k_tan.c \
e_acos.c e_acosh.c e_asin.c e_atan2.c \
e_atanh.c e_cosh.c e_exp.c e_fmod.c \
e_gamma.c e_gamma_r.c e_hypot.c e_j0.c \
e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c \
e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \
e_scalb.c e_sinh.c e_sqrt.c \
w_acos.c w_acosh.c w_asin.c w_atan2.c \
w_atanh.c w_cosh.c w_exp.c w_fmod.c \
w_gamma.c w_gamma_r.c w_hypot.c w_j0.c \
w_j1.c w_jn.c w_lgamma.c w_lgamma_r.c \
w_log.c w_log10.c w_pow.c w_remainder.c \
w_scalb.c w_sinh.c w_sqrt.c \
s_asinh.c s_atan.c s_cbrt.c s_ceil.c s_copysign.c \
s_cos.c s_erf.c s_expm1.c s_fabs.c s_finite.c s_floor.c \
s_frexp.c s_ilogb.c s_isnan.c s_ldexp.c s_lib_version.c \
s_log1p.c s_logb.c s_matherr.c s_modf.c s_nextafter.c \
s_rint.c s_scalbn.c s_signgam.c s_significand.c s_sin.c \
s_tan.c s_tanh.c
obj = k_standard.o k_rem_pio2.o \
k_cos.o k_sin.o k_tan.o \
e_acos.o e_acosh.o e_asin.o e_atan2.o \
e_atanh.o e_cosh.o e_exp.o e_fmod.o \
e_gamma.o e_gamma_r.o e_hypot.o e_j0.o \
e_j1.o e_jn.o e_lgamma.o e_lgamma_r.o \
e_log.o e_log10.o e_pow.o e_rem_pio2.o e_remainder.o \
e_scalb.o e_sinh.o e_sqrt.o \
w_acos.o w_acosh.o w_asin.o w_atan2.o \
w_atanh.o w_cosh.o w_exp.o w_fmod.o \
w_gamma.o w_gamma_r.o w_hypot.o w_j0.o \
w_j1.o w_jn.o w_lgamma.o w_lgamma_r.o \
w_log.o w_log10.o w_pow.o w_remainder.o \
w_scalb.o w_sinh.o w_sqrt.o \
s_asinh.o s_atan.o s_cbrt.o s_ceil.o s_copysign.o \
s_cos.o s_erf.o s_expm1.o s_fabs.o s_finite.o s_floor.o \
s_frexp.o s_ilogb.o s_isnan.o s_ldexp.o s_lib_version.o \
s_log1p.o s_logb.o s_matherr.o s_modf.o s_nextafter.o \
s_rint.o s_scalbn.o s_signgam.o s_significand.o s_sin.o \
s_tan.o s_tanh.o
all: libfdm.a
libfdm.a : $(obj)
ar cru libfdm.a $(obj)
ranlib libfdm.a
source: $(src) README
clean:
/bin/rm -f $(obj) a.out libfdm.a

View File

@@ -0,0 +1,105 @@
/* @(#)e_acos.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
#ifdef __STDC__
double __ieee754_acos(double x)
#else
double __ieee754_acos(x)
double x;
#endif
{
double z,p,q,r,w,s,c,df;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x3ff00000) { /* |x| >= 1 */
if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */
if(hx>0) return 0.0; /* acos(1) = 0 */
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
}
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(ix<0x3fe00000) { /* |x| < 0.5 */
if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
z = x*x;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (hx<0) { /* x < -0.5 */
z = (one+x)*0.5;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
s = fd_sqrt(z);
r = p/q;
w = r*s-pio2_lo;
return pi - 2.0*(s+w);
} else { /* x > 0.5 */
z = (one-x)*0.5;
s = fd_sqrt(z);
df = s;
__LO(df) = 0;
c = (z-df*df)/(s+df);
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
w = r*s+c;
return 2.0*(df+w);
}
}

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/* @(#)e_acosh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_acosh(x)
* Method :
* Based on
* acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
* acosh(x) := log(x)+ln2, if x is large; else
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acosh(x) is NaN with signal if x<1.
* acosh(NaN) is NaN without signal.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
#ifdef __STDC__
double __ieee754_acosh(double x)
#else
double __ieee754_acosh(x)
double x;
#endif
{
double t;
int hx;
hx = __HI(x);
if(hx<0x3ff00000) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x41b00000) { /* x > 2**28 */
if(hx >=0x7ff00000) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
} else if(((hx-0x3ff00000)|__LO(x))==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_log(2.0*x-one/(x+fd_sqrt(t-one)));
} else { /* 1<x<2 */
t = x-one;
return fd_log1p(t+fd_sqrt(2.0*t+t*t));
}
}

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/* @(#)e_asin.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* where
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
* and its remez error is bounded by
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
*
* For x in [0.5,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
* then for x>0.98
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
* For x<=0.98, let pio4_hi = pio2_hi/2, then
* f = hi part of s;
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
* and
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
huge = 1.000e+300,
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
/* coefficient for R(x^2) */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
#ifdef __STDC__
double __ieee754_asin(double x)
#else
double __ieee754_asin(x)
double x;
#endif
{
double t,w,p,q,c,r,s;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>= 0x3ff00000) { /* |x|>= 1 */
if(((ix-0x3ff00000)|__LO(x))==0)
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3fe00000) { /* |x|<0.5 */
if(ix<0x3e400000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
/* 1> |x|>= 0.5 */
w = one-fd_fabs(x);
t = w*0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = fd_sqrt(t);
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
w = p/q;
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
} else {
w = s;
__LO(w) = 0;
c = (t-w*w)/(s+w);
r = p/q;
p = 2.0*s*r-(pio2_lo-2.0*c);
q = pio4_hi-2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}

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/* @(#)e_atan2.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_atan2(y,x)
* Method :
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
tiny = 1.0e-300,
zero = 0.0,
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
#ifdef __STDC__
double __ieee754_atan2(double y, double x)
#else
double __ieee754_atan2(y,x)
double y,x;
#endif
{
double z;
int k,m,hx,hy,ix,iy;
unsigned lx,ly;
hx = __HI(x); ix = hx&0x7fffffff;
lx = __LO(x);
hy = __HI(y); iy = hy&0x7fffffff;
ly = __LO(y);
if(((ix|((lx|-(int)lx)>>31))>0x7ff00000)||
((iy|((ly|-(int)ly)>>31))>0x7ff00000)) /* x or y is NaN */
return x+y;
if((hx-0x3ff00000|lx)==0) return fd_atan(y); /* x=1.0 */
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if((iy|ly)==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7ff00000) {
if(iy==0x7ff00000) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* compute y/x */
k = (iy-ix)>>20;
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
else z=fd_atan(fd_fabs(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: __HI(z) ^= 0x80000000;
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}

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/* @(#)e_atanh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_atanh(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
*
* Special cases:
* atanh(x) is NaN if |x| > 1 with signal;
* atanh(NaN) is that NaN with no signal;
* atanh(+-1) is +-INF with signal.
*
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, huge = 1e300;
#else
static double one = 1.0, huge = 1e300;
#endif
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_atanh(double x)
#else
double __ieee754_atanh(x)
double x;
#endif
{
double t;
int hx,ix;
unsigned lx;
hx = __HI(x); /* high word */
lx = __LO(x); /* low word */
ix = hx&0x7fffffff;
if ((ix|((lx|(-(int)lx))>>31))>0x3ff00000) /* |x|>1 */
return (x-x)/(x-x);
if(ix==0x3ff00000)
return x/zero;
if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
__HI(x) = ix; /* x <- |x| */
if(ix<0x3fe00000) { /* x < 0.5 */
t = x+x;
t = 0.5*fd_log1p(t+t*x/(one-x));
} else
t = 0.5*fd_log1p((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}

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/* @(#)e_cosh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_cosh(x)
* Method :
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : cosh(x) := -------------------
* 2
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*/
#include "fdlibm.h"
#ifdef _WIN32
#define huge myhuge
#endif
#ifdef __STDC__
static const double one = 1.0, half=0.5, huge = 1.0e300;
#else
static double one = 1.0, half=0.5, huge = 1.0e300;
#endif
#ifdef __STDC__
double __ieee754_cosh(double x)
#else
double __ieee754_cosh(x)
double x;
#endif
{
double t,w;
int ix;
unsigned lx;
/* High word of |x|. */
ix = __HI(x);
ix &= 0x7fffffff;
/* x is INF or NaN */
if(ix>=0x7ff00000) return x*x;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e43) {
t = fd_expm1(fd_fabs(x));
w = one+t;
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x40360000) {
t = __ieee754_exp(fd_fabs(x));
return half*t+half/t;
}
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862E42) return half*__ieee754_exp(fd_fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
if (ix<0x408633CE ||
(ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
w = __ieee754_exp(half*fd_fabs(x));
t = half*w;
return t*w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}

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/* @(#)e_exp.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_exp(x)
* Returns the exponential of x.
*
* Method
* 1. Argument reduction:
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2.
*
* Here r will be represented as r = hi-lo for better
* accuracy.
*
* 2. Approximation of exp(r) by a special rational function on
* the interval [0,0.34658]:
* Write
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
* We use a special Reme algorithm on [0,0.34658] to generate
* a polynomial of degree 5 to approximate R. The maximum error
* of this polynomial approximation is bounded by 2**-59. In
* other words,
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
* (where z=r*r, and the values of P1 to P5 are listed below)
* and
* | 5 | -59
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
* | |
* The computation of exp(r) thus becomes
* 2*r
* exp(r) = 1 + -------
* R - r
* r*R1(r)
* = 1 + r + ----------- (for better accuracy)
* 2 - R1(r)
* where
* 2 4 10
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
*
* 3. Scale back to obtain exp(x):
* From step 1, we have
* exp(x) = 2^k * exp(r)
*
* Special cases:
* exp(INF) is INF, exp(NaN) is NaN;
* exp(-INF) is 0, and
* for finite argument, only exp(0)=1 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then exp(x) overflow
* if x < -7.45133219101941108420e+02 then exp(x) underflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
halF[2] = {0.5,-0.5,},
huge = 1.0e+300,
twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
#ifdef __STDC__
double __ieee754_exp(double x) /* default IEEE double exp */
#else
double __ieee754_exp(x) /* default IEEE double exp */
double x;
#endif
{
double y,hi,lo,c,t;
int k,xsb;
unsigned hx;
hx = __HI(x); /* high word of x */
xsb = (hx>>31)&1; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out non-finite argument */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
if(((hx&0xfffff)|__LO(x))!=0)
return x+x; /* NaN */
else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
}
if(x > o_threshold) return huge*huge; /* overflow */
if(x < u_threshold) return twom1000*twom1000; /* underflow */
}
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
} else {
k = (int)(invln2*x+halF[xsb]);
t = k;
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
lo = t*ln2LO[0];
}
x = hi - lo;
}
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
if(huge+x>one) return one+x;/* trigger inexact */
}
else k = 0;
/* x is now in primary range */
t = x*x;
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if(k==0) return one-((x*c)/(c-2.0)-x);
else y = one-((lo-(x*c)/(2.0-c))-hi);
if(k >= -1021) {
__HI(y) += (k<<20); /* add k to y's exponent */
return y;
} else {
__HI(y) += ((k+1000)<<20);/* add k to y's exponent */
return y*twom1000;
}
}

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/* @(#)e_fmod.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __ieee754_fmod(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, Zero[] = {0.0, -0.0,};
#else
static double one = 1.0, Zero[] = {0.0, -0.0,};
#endif
#ifdef __STDC__
double __ieee754_fmod(double x, double y)
#else
double __ieee754_fmod(x,y)
double x,y ;
#endif
{
int n,hx,hy,hz,ix,iy,sx,i;
unsigned lx,ly,lz;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
hy = __HI(y); /* high word of y */
ly = __LO(y); /* low word of y */
sx = hx&0x80000000; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
/* purge off exception values */
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
((hy|((ly|-(int)ly)>>31))>0x7ff00000)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<=hy) {
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
if(lx==ly)
return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(hx<0x00100000) { /* subnormal x */
if(hx==0) {
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
} else {
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
}
} else ix = (hx>>20)-1023;
/* determine iy = ilogb(y) */
if(hy<0x00100000) { /* subnormal y */
if(hy==0) {
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
} else {
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
}
} else iy = (hy>>20)-1023;
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -1022)
hx = 0x00100000|(0x000fffff&hx);
else { /* subnormal x, shift x to normal */
n = -1022-ix;
if(n<=31) {
hx = (hx<<n)|(lx>>(32-n));
lx <<= n;
} else {
hx = lx<<(n-32);
lx = 0;
}
}
if(iy >= -1022)
hy = 0x00100000|(0x000fffff&hy);
else { /* subnormal y, shift y to normal */
n = -1022-iy;
if(n<=31) {
hy = (hy<<n)|(ly>>(32-n));
ly <<= n;
} else {
hy = ly<<(n-32);
ly = 0;
}
}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
else {
if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(unsigned)sx>>31];
hx = hz+hz+(lz>>31); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
/* convert back to floating value and restore the sign */
if((hx|lx)==0) /* return sign(x)*0 */
return Zero[(unsigned)sx>>31];
while(hx<0x00100000) { /* normalize x */
hx = hx+hx+(lx>>31); lx = lx+lx;
iy -= 1;
}
if(iy>= -1022) { /* normalize output */
hx = ((hx-0x00100000)|((iy+1023)<<20));
__HI(x) = hx|sx;
__LO(x) = lx;
} else { /* subnormal output */
n = -1022 - iy;
if(n<=20) {
lx = (lx>>n)|((unsigned)hx<<(32-n));
hx >>= n;
} else if (n<=31) {
lx = (hx<<(32-n))|(lx>>n); hx = sx;
} else {
lx = hx>>(n-32); hx = sx;
}
__HI(x) = hx|sx;
__LO(x) = lx;
x *= one; /* create necessary signal */
}
return x; /* exact output */
}

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/* @(#)e_gamma.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_gamma(x)
* Return the logarithm of the Gamma function of x.
*
* Method: call __ieee754_gamma_r
*/
#include "fdlibm.h"
extern int signgam;
#ifdef __STDC__
double __ieee754_gamma(double x)
#else
double __ieee754_gamma(x)
double x;
#endif
{
return __ieee754_gamma_r(x,&signgam);
}

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/* @(#)e_gamma_r.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_gamma_r(x, signgamp)
* Reentrant version of the logarithm of the Gamma function
* with user provide pointer for the sign of Gamma(x).
*
* Method: See __ieee754_lgamma_r
*/
#include "fdlibm.h"
#ifdef __STDC__
double __ieee754_gamma_r(double x, int *signgamp)
#else
double __ieee754_gamma_r(x,signgamp)
double x; int *signgamp;
#endif
{
return __ieee754_lgamma_r(x,signgamp);
}

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/* @(#)e_hypot.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_hypot(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrt(2)/2 ulp, than
* sqrt(z) has error less than 1 ulp (exercise).
*
* So, compute sqrt(x*x+y*y) with some care as
* follows to get the error below 1 ulp:
*
* Assume x>y>0;
* (if possible, set rounding to round-to-nearest)
* 1. if x > 2y use
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
* 2. if x <= 2y use
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
* y1= y with lower 32 bits chopped, y2 = y-y1.
*
* NOTE: scaling may be necessary if some argument is too
* large or too tiny
*
* Special cases:
* hypot(x,y) is INF if x or y is +INF or -INF; else
* hypot(x,y) is NAN if x or y is NAN.
*
* Accuracy:
* hypot(x,y) returns sqrt(x^2+y^2) with error less
* than 1 ulps (units in the last place)
*/
#include "fdlibm.h"
#ifdef __STDC__
double __ieee754_hypot(double x, double y)
#else
double __ieee754_hypot(x,y)
double x, y;
#endif
{
double a=x,b=y,t1,t2,y1,y2,w;
int j,k,ha,hb;
ha = __HI(x)&0x7fffffff; /* high word of x */
hb = __HI(y)&0x7fffffff; /* high word of y */
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
__HI(a) = ha; /* a <- |a| */
__HI(b) = hb; /* b <- |b| */
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
k=0;
if(ha > 0x5f300000) { /* a>2**500 */
if(ha >= 0x7ff00000) { /* Inf or NaN */
w = a+b; /* for sNaN */
if(((ha&0xfffff)|__LO(a))==0) w = a;
if(((hb^0x7ff00000)|__LO(b))==0) w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x25800000; hb -= 0x25800000; k += 600;
__HI(a) = ha;
__HI(b) = hb;
}
if(hb < 0x20b00000) { /* b < 2**-500 */
if(hb <= 0x000fffff) { /* subnormal b or 0 */
if((hb|(__LO(b)))==0) return a;
t1=0;
__HI(t1) = 0x7fd00000; /* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
} else { /* scale a and b by 2^600 */
ha += 0x25800000; /* a *= 2^600 */
hb += 0x25800000; /* b *= 2^600 */
k -= 600;
__HI(a) = ha;
__HI(b) = hb;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
__HI(t1) = ha;
t2 = a-t1;
w = fd_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
__HI(y1) = hb;
y2 = b - y1;
t1 = 0;
__HI(t1) = ha+0x00100000;
t2 = a - t1;
w = fd_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
t1 = 1.0;
__HI(t1) += (k<<20);
return t1*w;
} else return w;
}

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/* @(#)e_j0.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_j0(x), __ieee754_y0(x)
* Bessel function of the first and second kinds of order zero.
* Method -- j0(x):
* 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
* 2. Reduce x to |x| since j0(x)=j0(-x), and
* for x in (0,2)
* j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
* (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
* for x in (2,inf)
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* as follow:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (cos(x) + sin(x))
* sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
*
* 3 Special cases
* j0(nan)= nan
* j0(0) = 1
* j0(inf) = 0
*
* Method -- y0(x):
* 1. For x<2.
* Since
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
* We use the following function to approximate y0,
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
* where
* U(z) = u00 + u01*z + ... + u06*z^6
* V(z) = 1 + v01*z + ... + v04*z^4
* with absolute approximation error bounded by 2**-72.
* Note: For tiny x, U/V = u0 and j0(x)~1, hence
* y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
* 2. For x>=2.
* y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* by the method mentioned above.
* 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
*/
#include "fdlibm.h"
#ifdef __STDC__
static double pzero(double), qzero(double);
#else
static double pzero(), qzero();
#endif
#ifdef __STDC__
static const double
#else
static double
#endif
huge = 1e300,
one = 1.0,
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
/* R0/S0 on [0, 2.00] */
R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_j0(double x)
#else
double __ieee754_j0(x)
double x;
#endif
{
double z, s,c,ss,cc,r,u,v;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/(x*x);
x = fd_fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = fd_sin(x);
c = fd_cos(x);
ss = s-c;
cc = s+c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -fd_cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(x);
}
return z;
}
if(ix<0x3f200000) { /* |x| < 2**-13 */
if(huge+x>one) { /* raise inexact if x != 0 */
if(ix<0x3e400000) return one; /* |x|<2**-27 */
else return one - 0.25*x*x;
}
}
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
if(ix < 0x3FF00000) { /* |x| < 1.00 */
return one + z*(-0.25+(r/s));
} else {
u = 0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
#ifdef __STDC__
static const double
#else
static double
#endif
u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
#ifdef __STDC__
double __ieee754_y0(double x)
#else
double __ieee754_y0(x)
double x;
#endif
{
double z, s,c,ss,cc,u,v;
int hx,ix,lx;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
s = fd_sin(x);
c = fd_cos(x);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -fd_cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x);
}
return z;
}
if(ix<=0x3e400000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_log(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
}
/* The asymptotic expansions of pzero is
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
* For x >= 2, We approximate pzero by
* pzero(x) = 1 + (R/S)
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
* S = 1 + pS0*s^2 + ... + pS4*s^10
* and
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
*/
#ifdef __STDC__
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
-8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
-2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
-2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
-5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
};
#ifdef __STDC__
static const double pS8[5] = {
#else
static double pS8[5] = {
#endif
1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
};
#ifdef __STDC__
static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
-1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
-7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
-4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
-6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
-3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
-3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
};
#ifdef __STDC__
static const double pS5[5] = {
#else
static double pS5[5] = {
#endif
6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
};
#ifdef __STDC__
static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
-2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
-7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
-2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
-2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
-5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
-3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
};
#ifdef __STDC__
static const double pS3[5] = {
#else
static double pS3[5] = {
#endif
3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
};
#ifdef __STDC__
static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
-8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
-7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
-1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
-7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
-1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
-3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
};
#ifdef __STDC__
static const double pS2[5] = {
#else
static double pS2[5] = {
#endif
2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
};
#ifdef __STDC__
static double pzero(double x)
#else
static double pzero(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double z,r,s;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = pR8; q= pS8;}
else if(ix>=0x40122E8B){p = pR5; q= pS5;}
else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
else if(ix>=0x40000000){p = pR2; q= pS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
/* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
* We approximate pzero by
* qzero(x) = s*(-1.25 + (R/S))
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
* S = 1 + qS0*s^2 + ... + qS5*s^12
* and
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
*/
#ifdef __STDC__
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
};
#ifdef __STDC__
static const double qS8[6] = {
#else
static double qS8[6] = {
#endif
1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
-3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
};
#ifdef __STDC__
static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
};
#ifdef __STDC__
static const double qS5[6] = {
#else
static double qS5[6] = {
#endif
8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
-5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
};
#ifdef __STDC__
static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
};
#ifdef __STDC__
static const double qS3[6] = {
#else
static double qS3[6] = {
#endif
4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
-1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
};
#ifdef __STDC__
static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
};
#ifdef __STDC__
static const double qS2[6] = {
#else
static double qS2[6] = {
#endif
3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
-5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
};
#ifdef __STDC__
static double qzero(double x)
#else
static double qzero(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double s,r,z;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = qR8; q= qS8;}
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
else if(ix>=0x40000000){p = qR2; q= qS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (-.125 + r/s)/x;
}

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@@ -0,0 +1,477 @@
/* @(#)e_j1.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_j1(x), __ieee754_y1(x)
* Bessel function of the first and second kinds of order zero.
* Method -- j1(x):
* 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
* 2. Reduce x to |x| since j1(x)=-j1(-x), and
* for x in (0,2)
* j1(x) = x/2 + x*z*R0/S0, where z = x*x;
* (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
* for x in (2,inf)
* j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
* as follow:
* cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (sin(x) + cos(x))
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
*
* 3 Special cases
* j1(nan)= nan
* j1(0) = 0
* j1(inf) = 0
*
* Method -- y1(x):
* 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
* 2. For x<2.
* Since
* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
* We use the following function to approximate y1,
* y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
* where for x in [0,2] (abs err less than 2**-65.89)
* U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
* V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
* Note: For tiny x, 1/x dominate y1 and hence
* y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
* 3. For x>=2.
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
* by method mentioned above.
*/
#include "fdlibm.h"
#ifdef __STDC__
static double pone(double), qone(double);
#else
static double pone(), qone();
#endif
#ifdef __STDC__
static const double
#else
static double
#endif
huge = 1e300,
one = 1.0,
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
/* R0/S0 on [0,2] */
r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_j1(double x)
#else
double __ieee754_j1(x)
double x;
#endif
{
double z, s,c,ss,cc,r,u,v,y;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/x;
y = fd_fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = fd_sin(y);
c = fd_cos(y);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure y+y not overflow */
z = fd_cos(y+y);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/*
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(y);
else {
u = pone(y); v = qone(y);
z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(y);
}
if(hx<0) return -z;
else return z;
}
if(ix<0x3e400000) { /* |x|<2**-27 */
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
return(x*0.5+r/s);
}
#ifdef __STDC__
static const double U0[5] = {
#else
static double U0[5] = {
#endif
-1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
-1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
-9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
};
#ifdef __STDC__
static const double V0[5] = {
#else
static double V0[5] = {
#endif
1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
};
#ifdef __STDC__
double __ieee754_y1(double x)
#else
double __ieee754_y1(x)
double x;
#endif
{
double z, s,c,ss,cc,u,v;
int hx,ix,lx;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = fd_sin(x);
c = fd_cos(x);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = fd_cos(x+x);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x);
else {
u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x);
}
return z;
}
if(ix<=0x3c900000) { /* x < 2**-54 */
return(-tpi/x);
}
z = x*x;
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
}
/* For x >= 8, the asymptotic expansions of pone is
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
* We approximate pone by
* pone(x) = 1 + (R/S)
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
* S = 1 + ps0*s^2 + ... + ps4*s^10
* and
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
*/
#ifdef __STDC__
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
};
#ifdef __STDC__
static const double ps8[5] = {
#else
static double ps8[5] = {
#endif
1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
};
#ifdef __STDC__
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
};
#ifdef __STDC__
static const double ps5[5] = {
#else
static double ps5[5] = {
#endif
5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
};
#ifdef __STDC__
static const double pr3[6] = {
#else
static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
};
#ifdef __STDC__
static const double ps3[5] = {
#else
static double ps3[5] = {
#endif
3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
};
#ifdef __STDC__
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
};
#ifdef __STDC__
static const double ps2[5] = {
#else
static double ps2[5] = {
#endif
2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
};
#ifdef __STDC__
static double pone(double x)
#else
static double pone(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double z,r,s;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = pr8; q= ps8;}
else if(ix>=0x40122E8B){p = pr5; q= ps5;}
else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
else if(ix>=0x40000000){p = pr2; q= ps2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
/* For x >= 8, the asymptotic expansions of qone is
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
* We approximate pone by
* qone(x) = s*(0.375 + (R/S))
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
* S = 1 + qs1*s^2 + ... + qs6*s^12
* and
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
*/
#ifdef __STDC__
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
-1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
-7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
-1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
-4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
};
#ifdef __STDC__
static const double qs8[6] = {
#else
static double qs8[6] = {
#endif
1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
-2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
};
#ifdef __STDC__
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
-2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
-1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
-8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
-1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
-1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
-2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
};
#ifdef __STDC__
static const double qs5[6] = {
#else
static double qs5[6] = {
#endif
8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
-4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
};
#ifdef __STDC__
static const double qr3[6] = {
#else
static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
-5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
-1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
-4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
-5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
-2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
-2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
};
#ifdef __STDC__
static const double qs3[6] = {
#else
static double qs3[6] = {
#endif
4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
-1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
};
#ifdef __STDC__
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
-1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
-1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
-2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
-1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
-4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
-2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
};
#ifdef __STDC__
static const double qs2[6] = {
#else
static double qs2[6] = {
#endif
2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
-4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
};
#ifdef __STDC__
static double qone(double x)
#else
static double qone(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double s,r,z;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = qr8; q= qs8;}
else if(ix>=0x40122E8B){p = qr5; q= qs5;}
else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
else if(ix>=0x40000000){p = qr2; q= qs2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (.375 + r/s)/x;
}

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@@ -0,0 +1,272 @@
/* @(#)e_jn.c 1.4 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __ieee754_jn(n, x), __ieee754_yn(n, x)
* floating point Bessel's function of the 1st and 2nd kind
* of order n
*
* Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
* Note 2. About jn(n,x), yn(n,x)
* For n=0, j0(x) is called,
* for n=1, j1(x) is called,
* for n<x, forward recursion us used starting
* from values of j0(x) and j1(x).
* for n>x, a continued fraction approximation to
* j(n,x)/j(n-1,x) is evaluated and then backward
* recursion is used starting from a supposed value
* for j(n,x). The resulting value of j(0,x) is
* compared with the actual value to correct the
* supposed value of j(n,x).
*
* yn(n,x) is similar in all respects, except
* that forward recursion is used for all
* values of n>1.
*
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
static double zero = 0.00000000000000000000e+00;
#ifdef __STDC__
double __ieee754_jn(int n, double x)
#else
double __ieee754_jn(n,x)
int n; double x;
#endif
{
int i,hx,ix,lx, sgn;
double a, b, temp, di;
double z, w;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
* Thus, J(-n,x) = J(n,-x)
*/
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
/* if J(n,NaN) is NaN */
if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x;
if(n<0){
n = -n;
x = -x;
hx ^= 0x80000000;
}
if(n==0) return(__ieee754_j0(x));
if(n==1) return(__ieee754_j1(x));
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
x = fd_fabs(x);
if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
b = zero;
else if((double)n<=x) {
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if(ix>=0x52D00000) { /* x > 2**302 */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch(n&3) {
case 0: temp = fd_cos(x)+fd_sin(x); break;
case 1: temp = -fd_cos(x)+fd_sin(x); break;
case 2: temp = -fd_cos(x)-fd_sin(x); break;
case 3: temp = fd_cos(x)-fd_sin(x); break;
}
b = invsqrtpi*temp/fd_sqrt(x);
} else {
a = __ieee754_j0(x);
b = __ieee754_j1(x);
for(i=1;i<n;i++){
temp = b;
b = b*((double)(i+i)/x) - a; /* avoid underflow */
a = temp;
}
}
} else {
if(ix<0x3e100000) { /* x < 2**-29 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if(n>33) /* underflow */
b = zero;
else {
temp = x*0.5; b = temp;
for (a=one,i=2;i<=n;i++) {
a *= (double)i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b/a;
}
} else {
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
double t,v;
double q0,q1,h,tmp; int k,m;
w = (n+n)/(double)x; h = 2.0/(double)x;
q0 = w; z = w+h; q1 = w*z - 1.0; k=1;
while(q1<1.0e9) {
k += 1; z += h;
tmp = z*q1 - q0;
q0 = q1;
q1 = tmp;
}
m = n+n;
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
a = t;
b = one;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
v = two/x;
tmp = tmp*__ieee754_log(fd_fabs(v*tmp));
if(tmp<7.09782712893383973096e+02) {
for(i=n-1,di=(double)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
}
} else {
for(i=n-1,di=(double)(i+i);i>0;i--){
temp = b;
b *= di;
b = b/x - a;
a = temp;
di -= two;
/* scale b to avoid spurious overflow */
if(b>1e100) {
a /= b;
t /= b;
b = one;
}
}
}
b = (t*__ieee754_j0(x)/b);
}
}
if(sgn==1) return -b; else return b;
}
#ifdef __STDC__
double __ieee754_yn(int n, double x)
#else
double __ieee754_yn(n,x)
int n; double x;
#endif
{
int i,hx,ix,lx;
int sign;
double a, b, temp;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
/* if Y(n,NaN) is NaN */
if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x;
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
sign = 1;
if(n<0){
n = -n;
sign = 1 - ((n&1)<<1);
}
if(n==0) return(__ieee754_y0(x));
if(n==1) return(sign*__ieee754_y1(x));
if(ix==0x7ff00000) return zero;
if(ix>=0x52D00000) { /* x > 2**302 */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
switch(n&3) {
case 0: temp = fd_sin(x)-fd_cos(x); break;
case 1: temp = -fd_sin(x)-fd_cos(x); break;
case 2: temp = -fd_sin(x)+fd_cos(x); break;
case 3: temp = fd_sin(x)+fd_cos(x); break;
}
b = invsqrtpi*temp/fd_sqrt(x);
} else {
a = __ieee754_y0(x);
b = __ieee754_y1(x);
/* quit if b is -inf */
for(i=1;i<n&&(__HI(b) != 0xfff00000);i++){
temp = b;
b = ((double)(i+i)/x)*b - a;
a = temp;
}
}
if(sign>0) return b; else return -b;
}

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/* @(#)e_lgamma.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_lgamma(x)
* Return the logarithm of the Gamma function of x.
*
* Method: call __ieee754_lgamma_r
*/
#include "fdlibm.h"
extern int signgam;
#ifdef __STDC__
double __ieee754_lgamma(double x)
#else
double __ieee754_lgamma(x)
double x;
#endif
{
return __ieee754_lgamma_r(x,&signgam);
}

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/* @(#)e_lgamma_r.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_lgamma_r(x, signgamp)
* Reentrant version of the logarithm of the Gamma function
* with user provide pointer for the sign of Gamma(x).
*
* Method:
* 1. Argument Reduction for 0 < x <= 8
* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
* reduce x to a number in [1.5,2.5] by
* lgamma(1+s) = log(s) + lgamma(s)
* for example,
* lgamma(7.3) = log(6.3) + lgamma(6.3)
* = log(6.3*5.3) + lgamma(5.3)
* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
* 2. Polynomial approximation of lgamma around its
* minimun ymin=1.461632144968362245 to maintain monotonicity.
* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
* Let z = x-ymin;
* lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
* where
* poly(z) is a 14 degree polynomial.
* 2. Rational approximation in the primary interval [2,3]
* We use the following approximation:
* s = x-2.0;
* lgamma(x) = 0.5*s + s*P(s)/Q(s)
* with accuracy
* |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
* Our algorithms are based on the following observation
*
* zeta(2)-1 2 zeta(3)-1 3
* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
* 2 3
*
* where Euler = 0.5771... is the Euler constant, which is very
* close to 0.5.
*
* 3. For x>=8, we have
* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
* (better formula:
* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
* Let z = 1/x, then we approximation
* f(z) = lgamma(x) - (x-0.5)(log(x)-1)
* by
* 3 5 11
* w = w0 + w1*z + w2*z + w3*z + ... + w6*z
* where
* |w - f(z)| < 2**-58.74
*
* 4. For negative x, since (G is gamma function)
* -x*G(-x)*G(x) = pi/sin(pi*x),
* we have
* G(x) = pi/(sin(pi*x)*(-x)*G(-x))
* since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
* Hence, for x<0, signgam = sign(sin(pi*x)) and
* lgamma(x) = log(|Gamma(x)|)
* = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
* Note: one should avoid compute pi*(-x) directly in the
* computation of sin(pi*(-x)).
*
* 5. Special Cases
* lgamma(2+s) ~ s*(1-Euler) for tiny s
* lgamma(1)=lgamma(2)=0
* lgamma(x) ~ -log(x) for tiny x
* lgamma(0) = lgamma(inf) = inf
* lgamma(-integer) = +-inf
*
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
/* tt = -(tail of tf) */
tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
static double zero= 0.00000000000000000000e+00;
#ifdef __STDC__
static double sin_pi(double x)
#else
static double sin_pi(x)
double x;
#endif
{
double y,z;
int n,ix;
ix = 0x7fffffff&__HI(x);
if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
y = -x; /* x is assume negative */
/*
* argument reduction, make sure inexact flag not raised if input
* is an integer
*/
z = fd_floor(y);
if(z!=y) { /* inexact anyway */
y *= 0.5;
y = 2.0*(y - fd_floor(y)); /* y = |x| mod 2.0 */
n = (int) (y*4.0);
} else {
if(ix>=0x43400000) {
y = zero; n = 0; /* y must be even */
} else {
if(ix<0x43300000) z = y+two52; /* exact */
n = __LO(z)&1; /* lower word of z */
y = n;
n<<= 2;
}
}
switch (n) {
case 0: y = __kernel_sin(pi*y,zero,0); break;
case 1:
case 2: y = __kernel_cos(pi*(0.5-y),zero); break;
case 3:
case 4: y = __kernel_sin(pi*(one-y),zero,0); break;
case 5:
case 6: y = -__kernel_cos(pi*(y-1.5),zero); break;
default: y = __kernel_sin(pi*(y-2.0),zero,0); break;
}
return -y;
}
#ifdef __STDC__
double __ieee754_lgamma_r(double x, int *signgamp)
#else
double __ieee754_lgamma_r(x,signgamp)
double x; int *signgamp;
#endif
{
double t,y,z,nadj,p,p1,p2,p3,q,r,w;
int i,hx,lx,ix;
hx = __HI(x);
lx = __LO(x);
/* purge off +-inf, NaN, +-0, and negative arguments */
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x*x;
if((ix|lx)==0) return one/zero;
if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
if(hx<0) {
*signgamp = -1;
return -__ieee754_log(-x);
} else return -__ieee754_log(x);
}
if(hx<0) {
if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
return one/zero;
t = sin_pi(x);
if(t==zero) return one/zero; /* -integer */
nadj = __ieee754_log(pi/fd_fabs(t*x));
if(t<zero) *signgamp = -1;
x = -x;
}
/* purge off 1 and 2 */
if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
/* for x < 2.0 */
else if(ix<0x40000000) {
if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
r = -__ieee754_log(x);
if(ix>=0x3FE76944) {y = one-x; i= 0;}
else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
else {y = x; i=2;}
} else {
r = zero;
if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
else {y=x-one;i=2;}
}
switch(i) {
case 0:
z = y*y;
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
p = y*p1+p2;
r += (p-0.5*y); break;
case 1:
z = y*y;
w = z*y;
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
p = z*p1-(tt-w*(p2+y*p3));
r += (tf + p); break;
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
r += (-0.5*y + p1/p2);
}
}
else if(ix<0x40200000) { /* x < 8.0 */
i = (int)x;
t = zero;
y = x-(double)i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
r = half*y+p/q;
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
switch(i) {
case 7: z *= (y+6.0); /* FALLTHRU */
case 6: z *= (y+5.0); /* FALLTHRU */
case 5: z *= (y+4.0); /* FALLTHRU */
case 4: z *= (y+3.0); /* FALLTHRU */
case 3: z *= (y+2.0); /* FALLTHRU */
r += __ieee754_log(z); break;
}
/* 8.0 <= x < 2**58 */
} else if (ix < 0x43900000) {
t = __ieee754_log(x);
z = one/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
r = (x-half)*(t-one)+w;
} else
/* 2**58 <= x <= inf */
r = x*(__ieee754_log(x)-one);
if(hx<0) r = nadj - r;
return r;
}

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/* @(#)e_log.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_log(x)
* Return the logrithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log(1+f) = f - s*(f - R) (if f is not too large)
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
*
* 3. Finally, log(x) = k*ln2 + log(1+f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_log(double x)
#else
double __ieee754_log(x)
double x;
#endif
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int k,hx,i,j;
unsigned lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = __HI(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
k += (i>>20);
f = x-1.0;
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
if(f==zero) if(k==0) return zero; else {dk=(double)k;
return dk*ln2_hi+dk*ln2_lo;}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+f);
dk = (double)k;
z = s*s;
i = hx-0x6147a;
w = z*z;
j = 0x6b851-hx;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}

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/* @(#)e_log10.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_log10(x)
* Return the base 10 logarithm of x
*
* Method :
* Let log10_2hi = leading 40 bits of log10(2) and
* log10_2lo = log10(2) - log10_2hi,
* ivln10 = 1/log(10) rounded.
* Then
* n = ilogb(x),
* if(n<0) n = n+1;
* x = scalbn(x,-n);
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
*
* Note 1:
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
* mode must set to Round-to-Nearest.
* Note 2:
* [1/log(10)] rounded to 53 bits has error .198 ulps;
* log10 is monotonic at all binary break points.
*
* Special cases:
* log10(x) is NaN with signal if x < 0;
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
* log10(NaN) is that NaN with no signal;
* log10(10**N) = N for N=0,1,...,22.
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_log10(double x)
#else
double __ieee754_log10(x)
double x;
#endif
{
double y,z;
int i,k,hx;
unsigned lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = __HI(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
i = ((unsigned)k&0x80000000)>>31;
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
y = (double)(k+i);
__HI(x) = hx;
z = y*log10_2lo + ivln10*__ieee754_log(x);
return z+y*log10_2hi;
}

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/* @(#)e_pow.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_pow(x,y) return x**y
*
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 53-24 = 29 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
* 3. (anything) ** NAN is NAN
* 4. NAN ** (anything except 0) is NAN
* 5. +-(|x| > 1) ** +INF is +INF
* 6. +-(|x| > 1) ** -INF is +0
* 7. +-(|x| < 1) ** +INF is +0
* 8. +-(|x| < 1) ** -INF is +INF
* 9. +-1 ** +-INF is NAN
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
* 12. +0 ** (-anything except 0, NAN) is +INF
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
* 15. +INF ** (+anything except 0,NAN) is +INF
* 16. +INF ** (-anything except 0,NAN) is +0
* 17. -INF ** (anything) = -0 ** (-anything)
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
*
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
* pow(integer,integer)
* always returns the correct integer provided it is
* representable.
*
* Constants :
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero = 0.0,
one = 1.0,
two = 2.0,
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
huge = 1.0e300,
tiny = 1.0e-300,
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
#ifdef __STDC__
double __ieee754_pow(double x, double y)
#else
double __ieee754_pow(x,y)
double x, y;
#endif
{
double z,ax,z_h,z_l,p_h,p_l;
double y1,t1,t2,r,s,t,u,v,w;
int i,j,k,yisint,n;
int hx,hy,ix,iy;
unsigned lx,ly;
hx = __HI(x); lx = __LO(x);
hy = __HI(y); ly = __LO(y);
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
if((iy|ly)==0) return one;
/* +-NaN return x+y */
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
return x+y;
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(iy>=0x43400000) yisint = 2; /* even integer y */
else if(iy>=0x3ff00000) {
k = (iy>>20)-0x3ff; /* exponent */
if(k>20) {
j = ly>>(52-k);
if((j<<(52-k))==(int)ly) yisint = 2-(j&1);
} else if(ly==0) {
j = iy>>(20-k);
if((j<<(20-k))==iy) yisint = 2-(j&1);
}
}
}
/* special value of y */
if(ly==0) {
if (iy==0x7ff00000) { /* y is +-inf */
if(((ix-0x3ff00000)|lx)==0)
return y - y; /* inf**+-1 is NaN */
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3ff00000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3fe00000) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return fd_sqrt(x);
}
}
ax = fd_fabs(x);
/* special value of x */
if(lx==0) {
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3ff00000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
/* (x<0)**(non-int) is NaN */
if((((hx>>31)+1)|yisint)==0) return (x-x)/(x-x);
/* |y| is huge */
if(iy>0x41e00000) { /* if |y| > 2**31 */
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
}
/* over/underflow if x is not close to one */
if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = x-1; /* t has 20 trailing zeros */
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
v = t*ivln2_l-w*ivln2;
t1 = u+v;
__LO(t1) = 0;
t2 = v-(t1-u);
} else {
double s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if(ix<0x00100000)
{ax *= two53; n -= 53; ix = __HI(ax); }
n += ((ix)>>20)-0x3ff;
j = ix&0x000fffff;
/* determine interval */
ix = j|0x3ff00000; /* normalize ix */
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00100000;}
__HI(ax) = ix;
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one/(ax+bp[k]);
s = u*v;
s_h = s;
__LO(s_h) = 0;
/* t_h=ax+bp[k] High */
t_h = zero;
__HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
s2 = s*s;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+s);
s2 = s_h*s_h;
t_h = 3.0+s2+r;
__LO(t_h) = 0;
t_l = r-((t_h-3.0)-s2);
/* u+v = s*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*s;
/* 2/(3log2)*(s+...) */
p_h = u+v;
__LO(p_h) = 0;
p_l = v-(p_h-u);
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l*p_h+p_l*cp+dp_l[k];
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
__LO(t1) = 0;
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if((((hx>>31)+1)|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
__LO(y1) = 0;
p_l = (y-y1)*t1+y*t2;
p_h = y1*t1;
z = p_l+p_h;
j = __HI(z);
i = __LO(z);
if (j>=0x40900000) { /* z >= 1024 */
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
return s*huge*huge; /* overflow */
else {
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
}
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
return s*tiny*tiny; /* underflow */
else {
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
i = j&0x7fffffff;
k = (i>>20)-0x3ff;
n = 0;
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00100000>>(k+1));
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
t = zero;
__HI(t) = (n&~(0x000fffff>>k));
n = ((n&0x000fffff)|0x00100000)>>(20-k);
if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
__LO(t) = 0;
u = t*lg2_h;
v = (p_l-(t-p_h))*lg2+t*lg2_l;
z = u+v;
w = v-(z-u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-two)-(w+z*w);
z = one-(r-z);
j = __HI(z);
j += (n<<20);
if((j>>20)<=0) z = fd_scalbn(z,n); /* subnormal output */
else __HI(z) += (n<<20);
return s*z;
}

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/* @(#)e_rem_pio2.c 1.4 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __ieee754_rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
#include "fdlibm.h"
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
#ifdef __STDC__
static const int two_over_pi[] = {
#else
static int two_over_pi[] = {
#endif
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};
#ifdef __STDC__
static const int npio2_hw[] = {
#else
static int npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
};
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 33 bit of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
#ifdef __STDC__
int __ieee754_rem_pio2(double x, double *y)
#else
int __ieee754_rem_pio2(x,y)
double x,y[];
#endif
{
double z,w,t,r,fn;
double tx[3];
int e0,i,j,nx,n,ix,hx;
hx = __HI(x); /* high word of x */
ix = hx&0x7fffffff;
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
{y[0] = x; y[1] = 0; return 0;}
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
if(hx>0) {
z = x - pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z - pio2_1t;
y[1] = (z-y[0])-pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z -= pio2_2;
y[0] = z - pio2_2t;
y[1] = (z-y[0])-pio2_2t;
}
return 1;
} else { /* negative x */
z = x + pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z + pio2_1t;
y[1] = (z-y[0])+pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z += pio2_2;
y[0] = z + pio2_2t;
y[1] = (z-y[0])+pio2_2t;
}
return -1;
}
}
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
t = fd_fabs(x);
n = (int) (t*invpio2+half);
fn = (double)n;
r = t-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 85 bit */
if(n<32&&ix!=npio2_hw[n-1]) {
y[0] = r-w; /* quick check no cancellation */
} else {
j = ix>>20;
y[0] = r-w;
i = j-(((__HI(y[0]))>>20)&0x7ff);
if(i>16) { /* 2nd iteration needed, good to 118 */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
i = j-(((__HI(y[0]))>>20)&0x7ff);
if(i>49) { /* 3rd iteration need, 151 bits acc */
t = r; /* will cover all possible cases */
w = fn*pio2_3;
r = t-w;
w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
}
y[1] = (r-y[0])-w;
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
else return n;
}
/*
* all other (large) arguments
*/
if(ix>=0x7ff00000) { /* x is inf or NaN */
y[0]=y[1]=x-x; return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
__LO(z) = __LO(x);
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
__HI(z) = ix - (e0<<20);
for(i=0;i<2;i++) {
tx[i] = (double)((int)(z));
z = (z-tx[i])*two24;
}
tx[2] = z;
nx = 3;
while(tx[nx-1]==zero) nx--; /* skip zero term */
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
return n;
}

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/* @(#)e_remainder.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_remainder(x,p)
* Return :
* returns x REM p = x - [x/p]*p as if in infinite
* precise arithmetic, where [x/p] is the (infinite bit)
* integer nearest x/p (in half way case choose the even one).
* Method :
* Based on fmod() return x-[x/p]chopped*p exactlp.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
#ifdef __STDC__
double __ieee754_remainder(double x, double p)
#else
double __ieee754_remainder(x,p)
double x,p;
#endif
{
int hx,hp;
unsigned sx,lx,lp;
double p_half;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
hp = __HI(p); /* high word of p */
lp = __LO(p); /* low word of p */
sx = hx&0x80000000;
hp &= 0x7fffffff;
hx &= 0x7fffffff;
/* purge off exception values */
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7ff00000)|| /* x not finite */
((hp>=0x7ff00000)&& /* p is NaN */
(((hp-0x7ff00000)|lp)!=0)))
return (x*p)/(x*p);
if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return zero*x;
x = fd_fabs(x);
p = fd_fabs(p);
if (hp<0x00200000) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = 0.5*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
__HI(x) ^= sx;
return x;
}

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/* @(#)e_scalb.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __ieee754_scalb(x, fn) is provide for
* passing various standard test suite. One
* should use scalbn() instead.
*/
#include "fdlibm.h"
#ifdef _SCALB_INT
#ifdef __STDC__
double __ieee754_scalb(double x, int fn)
#else
double __ieee754_scalb(x,fn)
double x; int fn;
#endif
#else
#ifdef __STDC__
double __ieee754_scalb(double x, double fn)
#else
double __ieee754_scalb(x,fn)
double x, fn;
#endif
#endif
{
#ifdef _SCALB_INT
return fd_scalbn(x,fn);
#else
if (fd_isnan(x)||fd_isnan(fn)) return x*fn;
if (!fd_finite(fn)) {
if(fn>0.0) return x*fn;
else return x/(-fn);
}
if (fd_rint(fn)!=fn) return (fn-fn)/(fn-fn);
if ( fn > 65000.0) return fd_scalbn(x, 65000);
if (-fn > 65000.0) return fd_scalbn(x,-65000);
return fd_scalbn(x,(int)fn);
#endif
}

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/* @(#)e_sinh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_sinh(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
* 2
*
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : sinh(x) := x*shuge (overflow)
*
* Special cases:
* sinh(x) is |x| if x is +INF, -INF, or NaN.
* only sinh(0)=0 is exact for finite x.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, shuge = 1.0e307;
#else
static double one = 1.0, shuge = 1.0e307;
#endif
#ifdef __STDC__
double __ieee754_sinh(double x)
#else
double __ieee754_sinh(x)
double x;
#endif
{
double t,w,h;
int ix,jx;
unsigned lx;
/* High word of |x|. */
jx = __HI(x);
ix = jx&0x7fffffff;
/* x is INF or NaN */
if(ix>=0x7ff00000) return x+x;
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x40360000) { /* |x|<22 */
if (ix<0x3e300000) /* |x|<2**-28 */
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
t = fd_expm1(fd_fabs(x));
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42) return h*__ieee754_exp(fd_fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
w = __ieee754_exp(0.5*fd_fabs(x));
t = h*w;
return t*w;
}
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}

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/* @(#)e_sqrt.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_sqrt(x)
* Return correctly rounded sqrt.
* ------------------------------------------
* | Use the hardware sqrt if you have one |
* ------------------------------------------
* Method:
* Bit by bit method using integer arithmetic. (Slow, but portable)
* 1. Normalization
* Scale x to y in [1,4) with even powers of 2:
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
* sqrt(x) = 2^k * sqrt(y)
* 2. Bit by bit computation
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
* i 0
* i+1 2
* s = 2*q , and y = 2 * ( y - q ). (1)
* i i i i
*
* To compute q from q , one checks whether
* i+1 i
*
* -(i+1) 2
* (q + 2 ) <= y. (2)
* i
* -(i+1)
* If (2) is false, then q = q ; otherwise q = q + 2 .
* i+1 i i+1 i
*
* With some algebric manipulation, it is not difficult to see
* that (2) is equivalent to
* -(i+1)
* s + 2 <= y (3)
* i i
*
* The advantage of (3) is that s and y can be computed by
* i i
* the following recurrence formula:
* if (3) is false
*
* s = s , y = y ; (4)
* i+1 i i+1 i
*
* otherwise,
* -i -(i+1)
* s = s + 2 , y = y - s - 2 (5)
* i+1 i i+1 i i
*
* One may easily use induction to prove (4) and (5).
* Note. Since the left hand side of (3) contain only i+2 bits,
* it does not necessary to do a full (53-bit) comparison
* in (3).
* 3. Final rounding
* After generating the 53 bits result, we compute one more bit.
* Together with the remainder, we can decide whether the
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
* (it will never equal to 1/2ulp).
* The rounding mode can be detected by checking whether
* huge + tiny is equal to huge, and whether huge - tiny is
* equal to huge for some floating point number "huge" and "tiny".
*
* Special cases:
* sqrt(+-0) = +-0 ... exact
* sqrt(inf) = inf
* sqrt(-ve) = NaN ... with invalid signal
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
*
* Other methods : see the appended file at the end of the program below.
*---------------
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, tiny=1.0e-300;
#else
static double one = 1.0, tiny=1.0e-300;
#endif
#ifdef __STDC__
double __ieee754_sqrt(double x)
#else
double __ieee754_sqrt(x)
double x;
#endif
{
double z;
int sign = (int)0x80000000;
unsigned r,t1,s1,ix1,q1;
int ix0,s0,q,m,t,i;
ix0 = __HI(x); /* high word of x */
ix1 = __LO(x); /* low word of x */
/* take care of Inf and NaN */
if((ix0&0x7ff00000)==0x7ff00000) {
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
sqrt(-inf)=sNaN */
}
/* take care of zero */
if(ix0<=0) {
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
else if(ix0<0)
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
}
/* normalize x */
m = (ix0>>20);
if(m==0) { /* subnormal x */
while(ix0==0) {
m -= 21;
ix0 |= (ix1>>11); ix1 <<= 21;
}
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
m -= i-1;
ix0 |= (ix1>>(32-i));
ix1 <<= i;
}
m -= 1023; /* unbias exponent */
ix0 = (ix0&0x000fffff)|0x00100000;
if(m&1){ /* odd m, double x to make it even */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
}
m >>= 1; /* m = [m/2] */
/* generate sqrt(x) bit by bit */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
r = 0x00200000; /* r = moving bit from right to left */
while(r!=0) {
t = s0+r;
if(t<=ix0) {
s0 = t+r;
ix0 -= t;
q += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
r = sign;
while(r!=0) {
t1 = s1+r;
t = s0;
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
s1 = t1+r;
if(((int)(t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
ix0 -= t;
if (ix1 < t1) ix0 -= 1;
ix1 -= t1;
q1 += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
/* use floating add to find out rounding direction */
if((ix0|ix1)!=0) {
z = one-tiny; /* trigger inexact flag */
if (z>=one) {
z = one+tiny;
if (q1==(unsigned)0xffffffff) { q1=0; q += 1;}
else if (z>one) {
if (q1==(unsigned)0xfffffffe) q+=1;
q1+=2;
} else
q1 += (q1&1);
}
}
ix0 = (q>>1)+0x3fe00000;
ix1 = q1>>1;
if ((q&1)==1) ix1 |= sign;
ix0 += (m <<20);
__HI(z) = ix0;
__LO(z) = ix1;
return z;
}
/*
Other methods (use floating-point arithmetic)
-------------
(This is a copy of a drafted paper by Prof W. Kahan
and K.C. Ng, written in May, 1986)
Two algorithms are given here to implement sqrt(x)
(IEEE double precision arithmetic) in software.
Both supply sqrt(x) correctly rounded. The first algorithm (in
Section A) uses newton iterations and involves four divisions.
The second one uses reciproot iterations to avoid division, but
requires more multiplications. Both algorithms need the ability
to chop results of arithmetic operations instead of round them,
and the INEXACT flag to indicate when an arithmetic operation
is executed exactly with no roundoff error, all part of the
standard (IEEE 754-1985). The ability to perform shift, add,
subtract and logical AND operations upon 32-bit words is needed
too, though not part of the standard.
A. sqrt(x) by Newton Iteration
(1) Initial approximation
Let x0 and x1 be the leading and the trailing 32-bit words of
a floating point number x (in IEEE double format) respectively
1 11 52 ...widths
------------------------------------------------------
x: |s| e | f |
------------------------------------------------------
msb lsb msb lsb ...order
------------------------ ------------------------
x0: |s| e | f1 | x1: | f2 |
------------------------ ------------------------
By performing shifts and subtracts on x0 and x1 (both regarded
as integers), we obtain an 8-bit approximation of sqrt(x) as
follows.
k := (x0>>1) + 0x1ff80000;
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
Here k is a 32-bit integer and T1[] is an integer array containing
correction terms. Now magically the floating value of y (y's
leading 32-bit word is y0, the value of its trailing word is 0)
approximates sqrt(x) to almost 8-bit.
Value of T1:
static int T1[32]= {
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
(2) Iterative refinement
Apply Heron's rule three times to y, we have y approximates
sqrt(x) to within 1 ulp (Unit in the Last Place):
y := (y+x/y)/2 ... almost 17 sig. bits
y := (y+x/y)/2 ... almost 35 sig. bits
y := y-(y-x/y)/2 ... within 1 ulp
Remark 1.
Another way to improve y to within 1 ulp is:
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
2
(x-y )*y
y := y + 2* ---------- ...within 1 ulp
2
3y + x
This formula has one division fewer than the one above; however,
it requires more multiplications and additions. Also x must be
scaled in advance to avoid spurious overflow in evaluating the
expression 3y*y+x. Hence it is not recommended uless division
is slow. If division is very slow, then one should use the
reciproot algorithm given in section B.
(3) Final adjustment
By twiddling y's last bit it is possible to force y to be
correctly rounded according to the prevailing rounding mode
as follows. Let r and i be copies of the rounding mode and
inexact flag before entering the square root program. Also we
use the expression y+-ulp for the next representable floating
numbers (up and down) of y. Note that y+-ulp = either fixed
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
mode.
I := FALSE; ... reset INEXACT flag I
R := RZ; ... set rounding mode to round-toward-zero
z := x/y; ... chopped quotient, possibly inexact
If(not I) then { ... if the quotient is exact
if(z=y) {
I := i; ... restore inexact flag
R := r; ... restore rounded mode
return sqrt(x):=y.
} else {
z := z - ulp; ... special rounding
}
}
i := TRUE; ... sqrt(x) is inexact
If (r=RN) then z=z+ulp ... rounded-to-nearest
If (r=RP) then { ... round-toward-+inf
y = y+ulp; z=z+ulp;
}
y := y+z; ... chopped sum
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
I := i; ... restore inexact flag
R := r; ... restore rounded mode
return sqrt(x):=y.
(4) Special cases
Square root of +inf, +-0, or NaN is itself;
Square root of a negative number is NaN with invalid signal.
B. sqrt(x) by Reciproot Iteration
(1) Initial approximation
Let x0 and x1 be the leading and the trailing 32-bit words of
a floating point number x (in IEEE double format) respectively
(see section A). By performing shifs and subtracts on x0 and y0,
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
k := 0x5fe80000 - (x0>>1);
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
Here k is a 32-bit integer and T2[] is an integer array
containing correction terms. Now magically the floating
value of y (y's leading 32-bit word is y0, the value of
its trailing word y1 is set to zero) approximates 1/sqrt(x)
to almost 7.8-bit.
Value of T2:
static int T2[64]= {
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
(2) Iterative refinement
Apply Reciproot iteration three times to y and multiply the
result by x to get an approximation z that matches sqrt(x)
to about 1 ulp. To be exact, we will have
-1ulp < sqrt(x)-z<1.0625ulp.
... set rounding mode to Round-to-nearest
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
... special arrangement for better accuracy
z := x*y ... 29 bits to sqrt(x), with z*y<1
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
(a) the term z*y in the final iteration is always less than 1;
(b) the error in the final result is biased upward so that
-1 ulp < sqrt(x) - z < 1.0625 ulp
instead of |sqrt(x)-z|<1.03125ulp.
(3) Final adjustment
By twiddling y's last bit it is possible to force y to be
correctly rounded according to the prevailing rounding mode
as follows. Let r and i be copies of the rounding mode and
inexact flag before entering the square root program. Also we
use the expression y+-ulp for the next representable floating
numbers (up and down) of y. Note that y+-ulp = either fixed
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
mode.
R := RZ; ... set rounding mode to round-toward-zero
switch(r) {
case RN: ... round-to-nearest
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
break;
case RZ:case RM: ... round-to-zero or round-to--inf
R:=RP; ... reset rounding mod to round-to-+inf
if(x<z*z ... rounded up) z = z - ulp; else
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
break;
case RP: ... round-to-+inf
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
if(x>z*z ...chopped) z = z+ulp;
break;
}
Remark 3. The above comparisons can be done in fixed point. For
example, to compare x and w=z*z chopped, it suffices to compare
x1 and w1 (the trailing parts of x and w), regarding them as
two's complement integers.
...Is z an exact square root?
To determine whether z is an exact square root of x, let z1 be the
trailing part of z, and also let x0 and x1 be the leading and
trailing parts of x.
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
I := 1; ... Raise Inexact flag: z is not exact
else {
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
k := z1 >> 26; ... get z's 25-th and 26-th
fraction bits
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
}
R:= r ... restore rounded mode
return sqrt(x):=z.
If multiplication is cheaper then the foregoing red tape, the
Inexact flag can be evaluated by
I := i;
I := (z*z!=x) or I.
Note that z*z can overwrite I; this value must be sensed if it is
True.
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
zero.
--------------------
z1: | f2 |
--------------------
bit 31 bit 0
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
or even of logb(x) have the following relations:
-------------------------------------------------
bit 27,26 of z1 bit 1,0 of x1 logb(x)
-------------------------------------------------
00 00 odd and even
01 01 even
10 10 odd
10 00 even
11 01 even
-------------------------------------------------
(4) Special cases (see (4) of Section A).
*/

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/* @(#)fdlibm.h 1.5 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* Modified defines start here.. */
#ifdef _WIN32
#define huge myhuge
#define __LITTLE_ENDIAN
#endif
/* End here. The rest is the standard file. */
#ifdef __NEWVALID /* special setup for Sun test regime */
#if defined(i386) || defined(i486) || \
defined(intel) || defined(x86) || defined(i86pc)
#define __LITTLE_ENDIAN
#endif
#endif
#ifdef __LITTLE_ENDIAN
#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x
#define __HIp(x) *(1+(int*)x)
#define __LOp(x) *(int*)x
#else
#define __HI(x) *(int*)&x
#define __LO(x) *(1+(int*)&x)
#define __HIp(x) *(int*)x
#define __LOp(x) *(1+(int*)x)
#endif
#ifdef __STDC__
#define __P(p) p
#else
#define __P(p) ()
#endif
/*
* ANSI/POSIX
*/
extern int signgam;
#define MAXFLOAT ((float)3.40282346638528860e+38)
enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};
#define _LIB_VERSION_TYPE enum fdversion
#define _LIB_VERSION _fdlib_version
/* if global variable _LIB_VERSION is not desirable, one may
* change the following to be a constant by:
* #define _LIB_VERSION_TYPE const enum version
* In that case, after one initializes the value _LIB_VERSION (see
* s_lib_version.c) during compile time, it cannot be modified
* in the middle of a program
*/
extern _LIB_VERSION_TYPE _LIB_VERSION;
#define _IEEE_ fdlibm_ieee
#define _SVID_ fdlibm_svid
#define _XOPEN_ fdlibm_xopen
#define _POSIX_ fdlibm_posix
struct exception {
int type;
char *name;
double arg1;
double arg2;
double retval;
};
#define HUGE MAXFLOAT
/*
* set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
* (one may replace the following line by "#include <values.h>")
*/
#define X_TLOSS 1.41484755040568800000e+16
#define DOMAIN 1
#define SING 2
#define OVERFLOW 3
#define UNDERFLOW 4
#define TLOSS 5
#define PLOSS 6
/*
* ANSI/POSIX
*/
extern double fd_acos __P((double));
extern double fd_asin __P((double));
extern double fd_atan __P((double));
extern double fd_atan2 __P((double, double));
extern double fd_cos __P((double));
extern double fd_sin __P((double));
extern double fd_tan __P((double));
extern double fd_cosh __P((double));
extern double fd_sinh __P((double));
extern double fd_tanh __P((double));
extern double fd_exp __P((double));
extern double fd_frexp __P((double, int *));
extern double fd_ldexp __P((double, int));
extern double fd_log __P((double));
extern double fd_log10 __P((double));
extern double fd_modf __P((double, double *));
extern double fd_pow __P((double, double));
extern double fd_sqrt __P((double));
extern double fd_ceil __P((double));
extern double fd_fabs __P((double));
extern double fd_floor __P((double));
extern double fd_fmod __P((double, double));
extern double fd_erf __P((double));
extern double fd_erfc __P((double));
extern double fd_gamma __P((double));
extern double fd_hypot __P((double, double));
extern int fd_isnan __P((double));
extern int fd_finite __P((double));
extern double fd_j0 __P((double));
extern double fd_j1 __P((double));
extern double fd_jn __P((int, double));
extern double fd_lgamma __P((double));
extern double fd_y0 __P((double));
extern double fd_y1 __P((double));
extern double fd_yn __P((int, double));
extern double fd_acosh __P((double));
extern double fd_asinh __P((double));
extern double fd_atanh __P((double));
extern double fd_cbrt __P((double));
extern double fd_logb __P((double));
extern double fd_nextafter __P((double, double));
extern double fd_remainder __P((double, double));
#ifdef _SCALB_INT
extern double fd_scalb __P((double, int));
#else
extern double fd_scalb __P((double, double));
#endif
extern int fd_matherr __P((struct exception *));
/*
* IEEE Test Vector
*/
extern double significand __P((double));
/*
* Functions callable from C, intended to support IEEE arithmetic.
*/
extern double fd_copysign __P((double, double));
extern int fd_ilogb __P((double));
extern double fd_rint __P((double));
extern double fd_scalbn __P((double, int));
/*
* BSD math library entry points
*/
extern double fd_expm1 __P((double));
extern double fd_log1p __P((double));
/*
* Reentrant version of gamma & lgamma; passes signgam back by reference
* as the second argument; user must allocate space for signgam.
*/
#ifdef _REENTRANT
extern double gamma_r __P((double, int *));
extern double lgamma_r __P((double, int *));
#endif /* _REENTRANT */
/* ieee style elementary functions */
extern double __ieee754_sqrt __P((double));
extern double __ieee754_acos __P((double));
extern double __ieee754_acosh __P((double));
extern double __ieee754_log __P((double));
extern double __ieee754_atanh __P((double));
extern double __ieee754_asin __P((double));
extern double __ieee754_atan2 __P((double,double));
extern double __ieee754_exp __P((double));
extern double __ieee754_cosh __P((double));
extern double __ieee754_fmod __P((double,double));
extern double __ieee754_pow __P((double,double));
extern double __ieee754_lgamma_r __P((double,int *));
extern double __ieee754_gamma_r __P((double,int *));
extern double __ieee754_lgamma __P((double));
extern double __ieee754_gamma __P((double));
extern double __ieee754_log10 __P((double));
extern double __ieee754_sinh __P((double));
extern double __ieee754_hypot __P((double,double));
extern double __ieee754_j0 __P((double));
extern double __ieee754_j1 __P((double));
extern double __ieee754_y0 __P((double));
extern double __ieee754_y1 __P((double));
extern double __ieee754_jn __P((int,double));
extern double __ieee754_yn __P((int,double));
extern double __ieee754_remainder __P((double,double));
extern int __ieee754_rem_pio2 __P((double,double*));
#ifdef _SCALB_INT
extern double __ieee754_scalb __P((double,int));
#else
extern double __ieee754_scalb __P((double,double));
#endif
/* fdlibm kernel function */
extern double __kernel_standard __P((double,double,int));
extern double __kernel_sin __P((double,double,int));
extern double __kernel_cos __P((double,double));
extern double __kernel_tan __P((double,double,int));
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));

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Microsoft C/C++ program database 2.00

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/* @(#)k_cos.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __kernel_cos( x, y )
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
*
* Algorithm
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
* 3. cos(x) is approximated by a polynomial of degree 14 on
* [0,pi/4]
* 4 14
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
* where the remez error is
*
* | 2 4 6 8 10 12 14 | -58
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
* | |
*
* 4 6 8 10 12 14
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
* cos(x) = 1 - x*x/2 + r
* since cos(x+y) ~ cos(x) - sin(x)*y
* ~ cos(x) - x*y,
* a correction term is necessary in cos(x) and hence
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
* For better accuracy when x > 0.3, let qx = |x|/4 with
* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
* Then
* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
* magnitude of the latter is at least a quarter of x*x/2,
* thus, reducing the rounding error in the subtraction.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
#ifdef __STDC__
double __kernel_cos(double x, double y)
#else
double __kernel_cos(x, y)
double x,y;
#endif
{
double a,hz,z,r,qx;
int ix;
ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/
if(ix<0x3e400000) { /* if x < 2**27 */
if(((int)x)==0) return one; /* generate inexact */
}
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
if(ix < 0x3FD33333) /* if |x| < 0.3 */
return one - (0.5*z - (z*r - x*y));
else {
if(ix > 0x3fe90000) { /* x > 0.78125 */
qx = 0.28125;
} else {
__HI(qx) = ix-0x00200000; /* x/4 */
__LO(qx) = 0;
}
hz = 0.5*z-qx;
a = one-qx;
return a - (hz - (z*r-x*y));
}
}

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/* @(#)k_rem_pio2.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
* double x[],y[]; int e0,nx,prec; int ipio2[];
*
* __kernel_rem_pio2 return the last three digits of N with
* y = x - N*pi/2
* so that |y| < pi/2.
*
* The method is to compute the integer (mod 8) and fraction parts of
* (2/pi)*x without doing the full multiplication. In general we
* skip the part of the product that are known to be a huge integer (
* more accurately, = 0 mod 8 ). Thus the number of operations are
* independent of the exponent of the input.
*
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
*
* Input parameters:
* x[] The input value (must be positive) is broken into nx
* pieces of 24-bit integers in double precision format.
* x[i] will be the i-th 24 bit of x. The scaled exponent
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
* match x's up to 24 bits.
*
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
* e0 = ilogb(z)-23
* z = scalbn(z,-e0)
* for i = 0,1,2
* x[i] = floor(z)
* z = (z-x[i])*2**24
*
*
* y[] ouput result in an array of double precision numbers.
* The dimension of y[] is:
* 24-bit precision 1
* 53-bit precision 2
* 64-bit precision 2
* 113-bit precision 3
* The actual value is the sum of them. Thus for 113-bit
* precison, one may have to do something like:
*
* long double t,w,r_head, r_tail;
* t = (long double)y[2] + (long double)y[1];
* w = (long double)y[0];
* r_head = t+w;
* r_tail = w - (r_head - t);
*
* e0 The exponent of x[0]
*
* nx dimension of x[]
*
* prec an integer indicating the precision:
* 0 24 bits (single)
* 1 53 bits (double)
* 2 64 bits (extended)
* 3 113 bits (quad)
*
* ipio2[]
* integer array, contains the (24*i)-th to (24*i+23)-th
* bit of 2/pi after binary point. The corresponding
* floating value is
*
* ipio2[i] * 2^(-24(i+1)).
*
* External function:
* double scalbn(), floor();
*
*
* Here is the description of some local variables:
*
* jk jk+1 is the initial number of terms of ipio2[] needed
* in the computation. The recommended value is 2,3,4,
* 6 for single, double, extended,and quad.
*
* jz local integer variable indicating the number of
* terms of ipio2[] used.
*
* jx nx - 1
*
* jv index for pointing to the suitable ipio2[] for the
* computation. In general, we want
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
* is an integer. Thus
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
* Hence jv = max(0,(e0-3)/24).
*
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
*
* q[] double array with integral value, representing the
* 24-bits chunk of the product of x and 2/pi.
*
* q0 the corresponding exponent of q[0]. Note that the
* exponent for q[i] would be q0-24*i.
*
* PIo2[] double precision array, obtained by cutting pi/2
* into 24 bits chunks.
*
* f[] ipio2[] in floating point
*
* iq[] integer array by breaking up q[] in 24-bits chunk.
*
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
*
* ih integer. If >0 it indicates q[] is >= 0.5, hence
* it also indicates the *sign* of the result.
*
*/
/*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
#else
static int init_jk[] = {2,3,4,6};
#endif
#ifdef __STDC__
static const double PIo2[] = {
#else
static double PIo2[] = {
#endif
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
};
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.0,
one = 1.0,
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
#ifdef __STDC__
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
#else
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
double x[], y[]; int e0,nx,prec; int ipio2[];
#endif
{
int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
double z,fw,f[20],fq[20],q[20];
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx-1;
jv = (e0-3)/24; if(jv<0) jv=0;
q0 = e0-24*(jv+1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv-jx; m = jx+jk;
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
/* compute q[0],q[1],...q[jk] */
for (i=0;i<=jk;i++) {
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
fw = (double)((int)(twon24* z));
iq[i] = (int)(z-two24*fw);
z = q[j-1]+fw;
}
/* compute n */
z = fd_scalbn(z,q0); /* actual value of z */
z -= 8.0*fd_floor(z*0.125); /* trim off integer >= 8 */
n = (int) z;
z -= (double)n;
ih = 0;
if(q0>0) { /* need iq[jz-1] to determine n */
i = (iq[jz-1]>>(24-q0)); n += i;
iq[jz-1] -= i<<(24-q0);
ih = iq[jz-1]>>(23-q0);
}
else if(q0==0) ih = iq[jz-1]>>23;
else if(z>=0.5) ih=2;
if(ih>0) { /* q > 0.5 */
n += 1; carry = 0;
for(i=0;i<jz ;i++) { /* compute 1-q */
j = iq[i];
if(carry==0) {
if(j!=0) {
carry = 1; iq[i] = 0x1000000- j;
}
} else iq[i] = 0xffffff - j;
}
if(q0>0) { /* rare case: chance is 1 in 12 */
switch(q0) {
case 1:
iq[jz-1] &= 0x7fffff; break;
case 2:
iq[jz-1] &= 0x3fffff; break;
}
}
if(ih==2) {
z = one - z;
if(carry!=0) z -= fd_scalbn(one,q0);
}
}
/* check if recomputation is needed */
if(z==zero) {
j = 0;
for (i=jz-1;i>=jk;i--) j |= iq[i];
if(j==0) { /* need recomputation */
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
f[jx+i] = (double) ipio2[jv+i];
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz += k;
goto recompute;
}
}
/* chop off zero terms */
if(z==0.0) {
jz -= 1; q0 -= 24;
while(iq[jz]==0) { jz--; q0-=24;}
} else { /* break z into 24-bit if necessary */
z = fd_scalbn(z,-q0);
if(z>=two24) {
fw = (double)((int)(twon24*z));
iq[jz] = (int)(z-two24*fw);
jz += 1; q0 += 24;
iq[jz] = (int) fw;
} else iq[jz] = (int) z ;
}
/* convert integer "bit" chunk to floating-point value */
fw = fd_scalbn(one,q0);
for(i=jz;i>=0;i--) {
q[i] = fw*(double)iq[i]; fw*=twon24;
}
/* compute PIo2[0,...,jp]*q[jz,...,0] */
for(i=jz;i>=0;i--) {
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
fq[jz-i] = fw;
}
/* compress fq[] into y[] */
switch(prec) {
case 0:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
break;
case 1:
case 2:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
fw = fq[0]-fw;
for (i=1;i<=jz;i++) fw += fq[i];
y[1] = (ih==0)? fw: -fw;
break;
case 3: /* painful */
for (i=jz;i>0;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (i=jz;i>1;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
if(ih==0) {
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
} else {
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
}
}
return n&7;
}

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/* @(#)k_sin.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __kernel_sin( x, y, iy)
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
*
* Algorithm
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
* 3. sin(x) is approximated by a polynomial of degree 13 on
* [0,pi/4]
* 3 13
* sin(x) ~ x + S1*x + ... + S6*x
* where
*
* |sin(x) 2 4 6 8 10 12 | -58
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
* | x |
*
* 4. sin(x+y) = sin(x) + sin'(x')*y
* ~ sin(x) + (1-x*x/2)*y
* For better accuracy, let
* 3 2 2 2 2
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
* then 3 2
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
#ifdef __STDC__
double __kernel_sin(double x, double y, int iy)
#else
double __kernel_sin(x, y, iy)
double x,y; int iy; /* iy=0 if y is zero */
#endif
{
double z,r,v;
int ix;
ix = __HI(x)&0x7fffffff; /* high word of x */
if(ix<0x3e400000) /* |x| < 2**-27 */
{if((int)x==0) return x;} /* generate inexact */
z = x*x;
v = z*x;
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
if(iy==0) return x+v*(S1+z*r);
else return x-((z*(half*y-v*r)-y)-v*S1);
}

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@@ -0,0 +1,734 @@
/* @(#)k_standard.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
#include "fdlibm.h"
#include <errno.h>
#ifndef _USE_WRITE
#include <stdio.h> /* fputs(), stderr */
#define WRITE2(u,v) fputs(u, stderr)
#else /* !defined(_USE_WRITE) */
#include <unistd.h> /* write */
#define WRITE2(u,v) write(2, u, v)
#undef fflush
#endif /* !defined(_USE_WRITE) */
static double zero = 0.0; /* used as const */
/*
* Standard conformance (non-IEEE) on exception cases.
* Mapping:
* 1 -- acos(|x|>1)
* 2 -- asin(|x|>1)
* 3 -- atan2(+-0,+-0)
* 4 -- hypot overflow
* 5 -- cosh overflow
* 6 -- exp overflow
* 7 -- exp underflow
* 8 -- y0(0)
* 9 -- y0(-ve)
* 10-- y1(0)
* 11-- y1(-ve)
* 12-- yn(0)
* 13-- yn(-ve)
* 14-- lgamma(finite) overflow
* 15-- lgamma(-integer)
* 16-- log(0)
* 17-- log(x<0)
* 18-- log10(0)
* 19-- log10(x<0)
* 20-- pow(0.0,0.0)
* 21-- pow(x,y) overflow
* 22-- pow(x,y) underflow
* 23-- pow(0,negative)
* 24-- pow(neg,non-integral)
* 25-- sinh(finite) overflow
* 26-- sqrt(negative)
* 27-- fmod(x,0)
* 28-- remainder(x,0)
* 29-- acosh(x<1)
* 30-- atanh(|x|>1)
* 31-- atanh(|x|=1)
* 32-- scalb overflow
* 33-- scalb underflow
* 34-- j0(|x|>X_TLOSS)
* 35-- y0(x>X_TLOSS)
* 36-- j1(|x|>X_TLOSS)
* 37-- y1(x>X_TLOSS)
* 38-- jn(|x|>X_TLOSS, n)
* 39-- yn(x>X_TLOSS, n)
* 40-- gamma(finite) overflow
* 41-- gamma(-integer)
* 42-- pow(NaN,0.0)
*/
#ifdef __STDC__
double __kernel_standard(double x, double y, int type)
#else
double __kernel_standard(x,y,type)
double x,y; int type;
#endif
{
struct exception exc;
#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
#define HUGE_VAL inf
double inf = 0.0;
__HI(inf) = 0x7ff00000; /* set inf to infinite */
#endif
#ifdef _USE_WRITE
(void) fflush(stdout);
#endif
exc.arg1 = x;
exc.arg2 = y;
switch(type) {
case 1:
/* acos(|x|>1) */
exc.type = DOMAIN;
exc.name = "acos";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if(_LIB_VERSION == _SVID_) {
(void) WRITE2("acos: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 2:
/* asin(|x|>1) */
exc.type = DOMAIN;
exc.name = "asin";
exc.retval = zero;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if(_LIB_VERSION == _SVID_) {
(void) WRITE2("asin: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 3:
/* atan2(+-0,+-0) */
exc.arg1 = y;
exc.arg2 = x;
exc.type = DOMAIN;
exc.name = "atan2";
exc.retval = zero;
if(_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if(_LIB_VERSION == _SVID_) {
(void) WRITE2("atan2: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 4:
/* hypot(finite,finite) overflow */
exc.type = OVERFLOW;
exc.name = "hypot";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 5:
/* cosh(finite) overflow */
exc.type = OVERFLOW;
exc.name = "cosh";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 6:
/* exp(finite) overflow */
exc.type = OVERFLOW;
exc.name = "exp";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 7:
/* exp(finite) underflow */
exc.type = UNDERFLOW;
exc.name = "exp";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 8:
/* y0(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y0";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y0: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 9:
/* y0(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y0";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y0: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 10:
/* y1(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y1";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y1: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 11:
/* y1(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y1";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("y1: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 12:
/* yn(n,0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "yn";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("yn: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 13:
/* yn(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "yn";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("yn: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 14:
/* lgamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = "lgamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 15:
/* lgamma(-integer) or lgamma(0) */
exc.type = SING;
exc.name = "lgamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("lgamma: SING error\n", 19);
}
errno = EDOM;
}
break;
case 16:
/* log(0) */
exc.type = SING;
exc.name = "log";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log: SING error\n", 16);
}
errno = EDOM;
}
break;
case 17:
/* log(x<0) */
exc.type = DOMAIN;
exc.name = "log";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log: DOMAIN error\n", 18);
}
errno = EDOM;
}
break;
case 18:
/* log10(0) */
exc.type = SING;
exc.name = "log10";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log10: SING error\n", 18);
}
errno = EDOM;
}
break;
case 19:
/* log10(x<0) */
exc.type = DOMAIN;
exc.name = "log10";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("log10: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 20:
/* pow(0.0,0.0) */
/* error only if _LIB_VERSION == _SVID_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.retval = zero;
if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
else if (!fd_matherr(&exc)) {
(void) WRITE2("pow(0,0): DOMAIN error\n", 23);
errno = EDOM;
}
break;
case 21:
/* pow(x,y) overflow */
exc.type = OVERFLOW;
exc.name = "pow";
if (_LIB_VERSION == _SVID_) {
exc.retval = HUGE;
y *= 0.5;
if(x<zero&&fd_rint(y)!=y) exc.retval = -HUGE;
} else {
exc.retval = HUGE_VAL;
y *= 0.5;
if(x<zero&&fd_rint(y)!=y) exc.retval = -HUGE_VAL;
}
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 22:
/* pow(x,y) underflow */
exc.type = UNDERFLOW;
exc.name = "pow";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 23:
/* 0**neg */
exc.type = DOMAIN;
exc.name = "pow";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
}
errno = EDOM;
}
break;
case 24:
/* neg**non-integral */
exc.type = DOMAIN;
exc.name = "pow";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero; /* X/Open allow NaN */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
}
errno = EDOM;
}
break;
case 25:
/* sinh(finite) overflow */
exc.type = OVERFLOW;
exc.name = "sinh";
if (_LIB_VERSION == _SVID_)
exc.retval = ( (x>zero) ? HUGE : -HUGE);
else
exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 26:
/* sqrt(x<0) */
exc.type = DOMAIN;
exc.name = "sqrt";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("sqrt: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 27:
/* fmod(x,0) */
exc.type = DOMAIN;
exc.name = "fmod";
if (_LIB_VERSION == _SVID_)
exc.retval = x;
else
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("fmod: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 28:
/* remainder(x,0) */
exc.type = DOMAIN;
exc.name = "remainder";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("remainder: DOMAIN error\n", 24);
}
errno = EDOM;
}
break;
case 29:
/* acosh(x<1) */
exc.type = DOMAIN;
exc.name = "acosh";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("acosh: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 30:
/* atanh(|x|>1) */
exc.type = DOMAIN;
exc.name = "atanh";
exc.retval = zero/zero;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("atanh: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 31:
/* atanh(|x|=1) */
exc.type = SING;
exc.name = "atanh";
exc.retval = x/zero; /* sign(x)*inf */
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("atanh: SING error\n", 18);
}
errno = EDOM;
}
break;
case 32:
/* scalb overflow; SVID also returns +-HUGE_VAL */
exc.type = OVERFLOW;
exc.name = "scalb";
exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 33:
/* scalb underflow */
exc.type = UNDERFLOW;
exc.name = "scalb";
exc.retval = fd_copysign(zero,x);
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 34:
/* j0(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j0";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 35:
/* y0(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y0";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 36:
/* j1(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j1";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 37:
/* y1(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y1";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 38:
/* jn(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "jn";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 39:
/* yn(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "yn";
exc.retval = zero;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2(exc.name, 2);
(void) WRITE2(": TLOSS error\n", 14);
}
errno = ERANGE;
}
break;
case 40:
/* gamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = "gamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = ERANGE;
else if (!fd_matherr(&exc)) {
errno = ERANGE;
}
break;
case 41:
/* gamma(-integer) or gamma(0) */
exc.type = SING;
exc.name = "gamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (_LIB_VERSION == _POSIX_)
errno = EDOM;
else if (!fd_matherr(&exc)) {
if (_LIB_VERSION == _SVID_) {
(void) WRITE2("gamma: SING error\n", 18);
}
errno = EDOM;
}
break;
case 42:
/* pow(NaN,0.0) */
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.retval = x;
if (_LIB_VERSION == _IEEE_ ||
_LIB_VERSION == _POSIX_) exc.retval = 1.0;
else if (!fd_matherr(&exc)) {
errno = EDOM;
}
break;
}
return exc.retval;
}

View File

@@ -0,0 +1,125 @@
/* @(#)k_tan.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __kernel_tan( x, y, k )
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input k indicates whether tan (if k=1) or
* -1/tan (if k= -1) is returned.
*
* Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
* 3. tan(x) is approximated by a odd polynomial of degree 27 on
* [0,0.67434]
* 3 27
* tan(x) ~ x + T1*x + ... + T13*x
* where
*
* |tan(x) 2 4 26 | -59.2
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
* | x |
*
* Note: tan(x+y) = tan(x) + tan'(x)*y
* ~ tan(x) + (1+x*x)*y
* Therefore, for better accuracy in computing tan(x+y), let
* 3 2 2 2 2
* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
* then
* 3 2
* tan(x+y) = x + (T1*x + (x *(r+y)+y))
*
* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
T[] = {
3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
};
#ifdef __STDC__
double __kernel_tan(double x, double y, int iy)
#else
double __kernel_tan(x, y, iy)
double x,y; int iy;
#endif
{
double z,r,v,w,s;
int ix,hx;
hx = __HI(x); /* high word of x */
ix = hx&0x7fffffff; /* high word of |x| */
if(ix<0x3e300000) /* x < 2**-28 */
{if((int)x==0) { /* generate inexact */
if(((ix|__LO(x))|(iy+1))==0) return one/fd_fabs(x);
else return (iy==1)? x: -one/x;
}
}
if(ix>=0x3FE59428) { /* |x|>=0.6744 */
if(hx<0) {x = -x; y = -y;}
z = pio4-x;
w = pio4lo-y;
x = z+w; y = 0.0;
}
z = x*x;
w = z*z;
/* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
*/
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
s = z*x;
r = y + z*(s*(r+v)+y);
r += T[0]*s;
w = x+r;
if(ix>=0x3FE59428) {
v = (double)iy;
return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
}
if(iy==1) return w;
else { /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
double a,t;
z = w;
__LO(z) = 0;
v = r-(z - x); /* z+v = r+x */
t = a = -1.0/w; /* a = -1.0/w */
__LO(t) = 0;
s = 1.0+t*z;
return t+a*(s+t*v);
}
}

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/* @(#)s_asinh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* asinh(x)
* Method :
* Based on
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
* we have
* asinh(x) := x if 1+x*x=1,
* := sign(x)*(log(x)+ln2)) for large |x|, else
* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge= 1.00000000000000000000e+300;
#ifdef __STDC__
double fd_asinh(double x)
#else
double fd_asinh(x)
double x;
#endif
{
double t,w;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
if(ix< 0x3e300000) { /* |x|<2**-28 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x41b00000) { /* |x| > 2**28 */
w = __ieee754_log(fd_fabs(x))+ln2;
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
t = fd_fabs(x);
w = __ieee754_log(2.0*t+one/(fd_sqrt(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =fd_log1p(fd_fabs(x)+t/(one+fd_sqrt(one+t)));
}
if(hx>0) return w; else return -w;
}

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/* @(#)s_atan.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* atan(x)
* Method
* 1. Reduce x to positive by atan(x) = -atan(-x).
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
* is further reduced to one of the following intervals and the
* arctangent of t is evaluated by the corresponding formula:
*
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double atanhi[] = {
#else
static double atanhi[] = {
#endif
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};
#ifdef __STDC__
static const double atanlo[] = {
#else
static double atanlo[] = {
#endif
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};
#ifdef __STDC__
static const double aT[] = {
#else
static double aT[] = {
#endif
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
huge = 1.0e300;
#ifdef __STDC__
double fd_atan(double x)
#else
double fd_atan(x)
double x;
#endif
{
double w,s1,s2,z;
int ix,hx,id;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x44100000) { /* if |x| >= 2^66 */
if(ix>0x7ff00000||
(ix==0x7ff00000&&(__LO(x)!=0)))
return x+x; /* NaN */
if(hx>0) return atanhi[3]+atanlo[3];
else return -atanhi[3]-atanlo[3];
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
if (ix < 0x3e200000) { /* |x| < 2^-29 */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
} else {
x = fd_fabs(x);
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
id = 0; x = (2.0*x-one)/(2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
}
} else {
if (ix < 0x40038000) { /* |x| < 2.4375 */
id = 2; x = (x-1.5)/(one+1.5*x);
} else { /* 2.4375 <= |x| < 2^66 */
id = 3; x = -1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (hx<0)? -z:z;
}
}

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/* @(#)s_cbrt.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
#include "fdlibm.h"
/* cbrt(x)
* Return cube root of x
*/
#ifdef __STDC__
static const unsigned
#else
static unsigned
#endif
B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
#ifdef __STDC__
static const double
#else
static double
#endif
C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
#ifdef __STDC__
double fd_cbrt(double x)
#else
double fd_cbrt(x)
double x;
#endif
{
int hx;
double r,s,t=0.0,w;
unsigned sign;
hx = __HI(x); /* high word of x */
sign=hx&0x80000000; /* sign= sign(x) */
hx ^=sign;
if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
if((hx|__LO(x))==0)
return(x); /* cbrt(0) is itself */
__HI(x) = hx; /* x <- |x| */
/* rough cbrt to 5 bits */
if(hx<0x00100000) /* subnormal number */
{__HI(t)=0x43500000; /* set t= 2**54 */
t*=x; __HI(t)=__HI(t)/3+B2;
}
else
__HI(t)=hx/3+B1;
/* new cbrt to 23 bits, may be implemented in single precision */
r=t*t/x;
s=C+r*t;
t*=G+F/(s+E+D/s);
/* chopped to 20 bits and make it larger than cbrt(x) */
__LO(t)=0; __HI(t)+=0x00000001;
/* one step newton iteration to 53 bits with error less than 0.667 ulps */
s=t*t; /* t*t is exact */
r=x/s;
w=t+t;
r=(r-t)/(w+r); /* r-s is exact */
t=t+t*r;
/* retore the sign bit */
__HI(t) |= sign;
return(t);
}

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/* @(#)s_ceil.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* ceil(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to ceil(x).
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
#ifdef __STDC__
double fd_ceil(double x)
#else
double fd_ceil(x)
double x;
#endif
{
int i0,i1,j0;
unsigned i,j;
i0 = __HI(x);
i1 = __LO(x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0<0) {i0=0x80000000;i1=0;}
else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0>0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0>0) {
if(j0==20) i0+=1;
else {
j = i1 + (1<<(52-j0));
if((int)j<i1) i0+=1; /* got a carry */
i1 = j;
}
}
i1 &= (~i);
}
}
__HI(x) = i0;
__LO(x) = i1;
return x;
}

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/* @(#)s_copysign.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* copysign(double x, double y)
* copysign(x,y) returns a value with the magnitude of x and
* with the sign bit of y.
*/
#include "fdlibm.h"
#ifdef __STDC__
double fd_copysign(double x, double y)
#else
double fd_copysign(x,y)
double x,y;
#endif
{
__HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
return x;
}

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/* @(#)s_cos.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* cos(x)
* Return cosine function of x.
*
* kernel function:
* __kernel_sin ... sine function on [-pi/4,pi/4]
* __kernel_cos ... cosine function on [-pi/4,pi/4]
* __ieee754_rem_pio2 ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifdef __STDC__
double fd_cos(double x)
#else
double fd_cos(x)
double x;
#endif
{
double y[2],z=0.0;
int n, ix;
/* High word of x. */
ix = __HI(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
/* cos(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
switch(n&3) {
case 0: return __kernel_cos(y[0],y[1]);
case 1: return -__kernel_sin(y[0],y[1],1);
case 2: return -__kernel_cos(y[0],y[1]);
default:
return __kernel_sin(y[0],y[1],1);
}
}
}

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/* @(#)s_erf.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* double erf(double x)
* double erfc(double x)
* x
* 2 |\
* erf(x) = --------- | exp(-t*t)dt
* sqrt(pi) \|
* 0
*
* erfc(x) = 1-erf(x)
* Note that
* erf(-x) = -erf(x)
* erfc(-x) = 2 - erfc(x)
*
* Method:
* 1. For |x| in [0, 0.84375]
* erf(x) = x + x*R(x^2)
* erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
* = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
* where R = P/Q where P is an odd poly of degree 8 and
* Q is an odd poly of degree 10.
* -57.90
* | R - (erf(x)-x)/x | <= 2
*
*
* Remark. The formula is derived by noting
* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
* and that
* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
* is close to one. The interval is chosen because the fix
* point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
* near 0.6174), and by some experiment, 0.84375 is chosen to
* guarantee the error is less than one ulp for erf.
*
* 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
* c = 0.84506291151 rounded to single (24 bits)
* erf(x) = sign(x) * (c + P1(s)/Q1(s))
* erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
* 1+(c+P1(s)/Q1(s)) if x < 0
* |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
* Remark: here we use the taylor series expansion at x=1.
* erf(1+s) = erf(1) + s*Poly(s)
* = 0.845.. + P1(s)/Q1(s)
* That is, we use rational approximation to approximate
* erf(1+s) - (c = (single)0.84506291151)
* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
* where
* P1(s) = degree 6 poly in s
* Q1(s) = degree 6 poly in s
*
* 3. For x in [1.25,1/0.35(~2.857143)],
* erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
* erf(x) = 1 - erfc(x)
* where
* R1(z) = degree 7 poly in z, (z=1/x^2)
* S1(z) = degree 8 poly in z
*
* 4. For x in [1/0.35,28]
* erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
* = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
* = 2.0 - tiny (if x <= -6)
* erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
* erf(x) = sign(x)*(1.0 - tiny)
* where
* R2(z) = degree 6 poly in z, (z=1/x^2)
* S2(z) = degree 7 poly in z
*
* Note1:
* To compute exp(-x*x-0.5625+R/S), let s be a single
* precision number and s := x; then
* -x*x = -s*s + (s-x)*(s+x)
* exp(-x*x-0.5626+R/S) =
* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
* Note2:
* Here 4 and 5 make use of the asymptotic series
* exp(-x*x)
* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
* x*sqrt(pi)
* We use rational approximation to approximate
* g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
* Here is the error bound for R1/S1 and R2/S2
* |R1/S1 - f(x)| < 2**(-62.57)
* |R2/S2 - f(x)| < 2**(-61.52)
*
* 5. For inf > x >= 28
* erf(x) = sign(x) *(1 - tiny) (raise inexact)
* erfc(x) = tiny*tiny (raise underflow) if x > 0
* = 2 - tiny if x<0
*
* 7. Special case:
* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
* erfc/erf(NaN) is NaN
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
tiny = 1e-300,
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
#ifdef __STDC__
double fd_erf(double x)
#else
double fd_erf(x)
double x;
#endif
{
int hx,ix,i;
double R,S,P,Q,s,y,z,r;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) { /* erf(nan)=nan */
i = ((unsigned)hx>>31)<<1;
return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
if(ix < 0x3feb0000) { /* |x|<0.84375 */
if(ix < 0x3e300000) { /* |x|<2**-28 */
if (ix < 0x00800000)
return 0.125*(8.0*x+efx8*x); /*avoid underflow */
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
s = fd_fabs(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40180000) { /* inf>|x|>=6 */
if(hx>=0) return one-tiny; else return tiny-one;
}
x = fd_fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
z = x;
__LO(z) = 0;
r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S);
if(hx>=0) return one-r/x; else return r/x-one;
}
#ifdef __STDC__
double erfc(double x)
#else
double erfc(x)
double x;
#endif
{
int hx,ix;
double R,S,P,Q,s,y,z,r;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) { /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
return (double)(((unsigned)hx>>31)<<1)+one/x;
}
if(ix < 0x3feb0000) { /* |x|<0.84375 */
if(ix < 0x3c700000) /* |x|<2**-56 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
if(hx < 0x3fd00000) { /* x<1/4 */
return one-(x+x*y);
} else {
r = x*y;
r += (x-half);
return half - r ;
}
}
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
s = fd_fabs(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) {
z = one-erx; return z - P/Q;
} else {
z = erx+P/Q; return one+z;
}
}
if (ix < 0x403c0000) { /* |x|<28 */
x = fd_fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
z = x;
__LO(z) = 0;
r = __ieee754_exp(-z*z-0.5625)*
__ieee754_exp((z-x)*(z+x)+R/S);
if(hx>0) return r/x; else return two-r/x;
} else {
if(hx>0) return tiny*tiny; else return two-tiny;
}
}

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/* @(#)s_expm1.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* expm1(x)
* Returns exp(x)-1, the exponential of x minus 1.
*
* Method
* 1. Argument reduction:
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
*
* Here a correction term c will be computed to compensate
* the error in r when rounded to a floating-point number.
*
* 2. Approximating expm1(r) by a special rational function on
* the interval [0,0.34658]:
* Since
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
* we define R1(r*r) by
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
* That is,
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
* We use a special Reme algorithm on [0,0.347] to generate
* a polynomial of degree 5 in r*r to approximate R1. The
* maximum error of this polynomial approximation is bounded
* by 2**-61. In other words,
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
* where Q1 = -1.6666666666666567384E-2,
* Q2 = 3.9682539681370365873E-4,
* Q3 = -9.9206344733435987357E-6,
* Q4 = 2.5051361420808517002E-7,
* Q5 = -6.2843505682382617102E-9;
* (where z=r*r, and the values of Q1 to Q5 are listed below)
* with error bounded by
* | 5 | -61
* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
* | |
*
* expm1(r) = exp(r)-1 is then computed by the following
* specific way which minimize the accumulation rounding error:
* 2 3
* r r [ 3 - (R1 + R1*r/2) ]
* expm1(r) = r + --- + --- * [--------------------]
* 2 2 [ 6 - r*(3 - R1*r/2) ]
*
* To compensate the error in the argument reduction, we use
* expm1(r+c) = expm1(r) + c + expm1(r)*c
* ~ expm1(r) + c + r*c
* Thus c+r*c will be added in as the correction terms for
* expm1(r+c). Now rearrange the term to avoid optimization
* screw up:
* ( 2 2 )
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
* ( )
*
* = r - E
* 3. Scale back to obtain expm1(x):
* From step 1, we have
* expm1(x) = either 2^k*[expm1(r)+1] - 1
* = or 2^k*[expm1(r) + (1-2^-k)]
* 4. Implementation notes:
* (A). To save one multiplication, we scale the coefficient Qi
* to Qi*2^i, and replace z by (x^2)/2.
* (B). To achieve maximum accuracy, we compute expm1(x) by
* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
* (ii) if k=0, return r-E
* (iii) if k=-1, return 0.5*(r-E)-0.5
* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
* else return 1.0+2.0*(r-E);
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
* (vii) return 2^k(1-((E+2^-k)-r))
*
* Special cases:
* expm1(INF) is INF, expm1(NaN) is NaN;
* expm1(-INF) is -1, and
* for finite argument, only expm1(0)=0 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
huge = 1.0e+300,
tiny = 1.0e-300,
o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
/* scaled coefficients related to expm1 */
Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
#ifdef __STDC__
double fd_expm1(double x)
#else
double fd_expm1(x)
double x;
#endif
{
double y,hi,lo,c,t,e,hxs,hfx,r1;
int k,xsb;
unsigned hx;
hx = __HI(x); /* high word of x */
xsb = hx&0x80000000; /* sign bit of x */
if(xsb==0) y=x; else y= -x; /* y = |x| */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
if(((hx&0xfffff)|__LO(x))!=0)
return x+x; /* NaN */
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
}
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
if(x+tiny<0.0) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
if(xsb==0)
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
else
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
} else {
k = (int)(invln2*x+((xsb==0)?0.5:-0.5));
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
x = hi - lo;
c = (hi-x)-lo;
}
else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = 0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = 3.0-r1*hfx;
e = hxs*((r1-t)/(6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return 0.5*(x-e)-0.5;
if(k==1)
if(x < -0.25) return -2.0*(e-(x+0.5));
else return one+2.0*(x-e);
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
y = one-(e-x);
__HI(y) += (k<<20); /* add k to y's exponent */
return y-one;
}
t = one;
if(k<20) {
__HI(t) = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */
y = t-(e-x);
__HI(y) += (k<<20); /* add k to y's exponent */
} else {
__HI(t) = ((0x3ff-k)<<20); /* 2^-k */
y = x-(e+t);
y += one;
__HI(y) += (k<<20); /* add k to y's exponent */
}
}
return y;
}

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/* @(#)s_fabs.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* fabs(x) returns the absolute value of x.
*/
#include "fdlibm.h"
#ifdef __STDC__
double fd_fabs(double x)
#else
double fd_fabs(x)
double x;
#endif
{
__HI(x) &= 0x7fffffff;
return x;
}

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/* @(#)s_finite.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* finite(x) returns 1 is x is finite, else 0;
* no branching!
*/
#include "fdlibm.h"
#ifdef __STDC__
int fd_finite(double x)
#else
int fd_finite(x)
double x;
#endif
{
int hx;
hx = __HI(x);
return (unsigned)((hx&0x7fffffff)-0x7ff00000)>>31;
}

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/* @(#)s_floor.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* floor(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floor(x).
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
#ifdef __STDC__
double fd_floor(double x)
#else
double fd_floor(x)
double x;
#endif
{
int i0,i1,j0;
unsigned i,j;
i0 = __HI(x);
i1 = __LO(x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0>=0) {i0=i1=0;}
else if(((i0&0x7fffffff)|i1)!=0)
{ i0=0xbff00000;i1=0;}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) {
if(j0==20) i0+=1;
else {
j = i1+(1<<(52-j0));
if((int)j<i1) i0 +=1 ; /* got a carry */
i1=j;
}
}
i1 &= (~i);
}
}
__HI(x) = i0;
__LO(x) = i1;
return x;
}

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/* @(#)s_frexp.c 1.4 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* for non-zero x
* x = frexp(arg,&exp);
* return a double fp quantity x such that 0.5 <= |x| <1.0
* and the corresponding binary exponent "exp". That is
* arg = x*2^exp.
* If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg
* with *exp=0.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
#ifdef __STDC__
double fd_frexp(double x, int *eptr)
#else
double fd_frexp(x, eptr)
double x; int *eptr;
#endif
{
int hx, ix, lx;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
*eptr = 0;
if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */
if (ix<0x00100000) { /* subnormal */
x *= two54;
hx = __HI(x);
ix = hx&0x7fffffff;
*eptr = -54;
}
*eptr += (ix>>20)-1022;
hx = (hx&0x800fffff)|0x3fe00000;
__HI(x) = hx;
return x;
}

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/* @(#)s_ilogb.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* ilogb(double x)
* return the binary exponent of non-zero x
* ilogb(0) = 0x80000001
* ilogb(inf/NaN) = 0x7fffffff (no signal is raised)
*/
#include "fdlibm.h"
#ifdef __STDC__
int fd_ilogb(double x)
#else
int fd_ilogb(x)
double x;
#endif
{
int hx,lx,ix;
hx = (__HI(x))&0x7fffffff; /* high word of x */
if(hx<0x00100000) {
lx = __LO(x);
if((hx|lx)==0)
return 0x80000001; /* ilogb(0) = 0x80000001 */
else /* subnormal x */
if(hx==0) {
for (ix = -1043; lx>0; lx<<=1) ix -=1;
} else {
for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
}
return ix;
}
else if (hx<0x7ff00000) return (hx>>20)-1023;
else return 0x7fffffff;
}

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/* @(#)s_isnan.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* isnan(x) returns 1 is x is nan, else 0;
* no branching!
*/
#include "fdlibm.h"
#ifdef __STDC__
int fd_isnan(double x)
#else
int fd_isnan(x)
double x;
#endif
{
int hx,lx;
hx = (__HI(x)&0x7fffffff);
lx = __LO(x);
hx |= (unsigned)(lx|(-lx))>>31;
hx = 0x7ff00000 - hx;
return ((unsigned)(hx))>>31;
}

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/* @(#)s_ldexp.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include "fdlibm.h"
#include <errno.h>
#ifdef __STDC__
double fd_ldexp(double value, int exp)
#else
double fd_ldexp(value, exp)
double value; int exp;
#endif
{
if(!fd_finite(value)||value==0.0) return value;
value = fd_scalbn(value,exp);
if(!fd_finite(value)||value==0.0) errno = ERANGE;
return value;
}

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/* @(#)s_lib_version.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* MACRO for standards
*/
#include "fdlibm.h"
/*
* define and initialize _LIB_VERSION
*/
#ifdef _POSIX_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_;
#else
#ifdef _XOPEN_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_;
#else
#ifdef _SVID3_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _SVID_;
#else /* default _IEEE_MODE */
_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_;
#endif
#endif
#endif

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/* @(#)s_log1p.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* double log1p(double x)
*
* Method :
* 1. Argument Reduction: find k and f such that
* 1+x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* Note. If k=0, then f=x is exact. However, if k!=0, then f
* may not be representable exactly. In that case, a correction
* term is need. Let u=1+x rounded. Let c = (1+x)-u, then
* log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
* and add back the correction term c/u.
* (Note: when x > 2**53, one can simply return log(x))
*
* 2. Approximation of log1p(f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
* (the values of Lp1 to Lp7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lp1*s +...+Lp7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log1p(f) = f - (hfsq - s*(hfsq+R)).
*
* 3. Finally, log1p(x) = k*ln2 + log1p(f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log1p(x) is NaN with signal if x < -1 (including -INF) ;
* log1p(+INF) is +INF; log1p(-1) is -INF with signal;
* log1p(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*
* Note: Assuming log() return accurate answer, the following
* algorithm can be used to compute log1p(x) to within a few ULP:
*
* u = 1+x;
* if(u==1.0) return x ; else
* return log(u)*(x/(u-1.0));
*
* See HP-15C Advanced Functions Handbook, p.193.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static double zero = 0.0;
#ifdef __STDC__
double fd_log1p(double x)
#else
double fd_log1p(x)
double x;
#endif
{
double hfsq,f,c,s,z,R,u;
int k,hx,hu,ax;
hx = __HI(x); /* high word of x */
ax = hx&0x7fffffff;
k = 1;
if (hx < 0x3FDA827A) { /* x < 0.41422 */
if(ax>=0x3ff00000) { /* x <= -1.0 */
if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */
else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
}
if(ax<0x3e200000) { /* |x| < 2**-29 */
if(two54+x>zero /* raise inexact */
&&ax<0x3c900000) /* |x| < 2**-54 */
return x;
else
return x - x*x*0.5;
}
if(hx>0||hx<=((int)0xbfd2bec3)) {
k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
}
if (hx >= 0x7ff00000) return x+x;
if(k!=0) {
if(hx<0x43400000) {
u = 1.0+x;
hu = __HI(u); /* high word of u */
k = (hu>>20)-1023;
c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
c /= u;
} else {
u = x;
hu = __HI(u); /* high word of u */
k = (hu>>20)-1023;
c = 0;
}
hu &= 0x000fffff;
if(hu<0x6a09e) {
__HI(u) = hu|0x3ff00000; /* normalize u */
} else {
k += 1;
__HI(u) = hu|0x3fe00000; /* normalize u/2 */
hu = (0x00100000-hu)>>2;
}
f = u-1.0;
}
hfsq=0.5*f*f;
if(hu==0) { /* |f| < 2**-20 */
if(f==zero) if(k==0) return zero;
else {c += k*ln2_lo; return k*ln2_hi+c;}
R = hfsq*(1.0-0.66666666666666666*f);
if(k==0) return f-R; else
return k*ln2_hi-((R-(k*ln2_lo+c))-f);
}
s = f/(2.0+f);
z = s*s;
R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}

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/* @(#)s_logb.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* double logb(x)
* IEEE 754 logb. Included to pass IEEE test suite. Not recommend.
* Use ilogb instead.
*/
#include "fdlibm.h"
#ifdef __STDC__
double fd_logb(double x)
#else
double fd_logb(x)
double x;
#endif
{
int lx,ix;
ix = (__HI(x))&0x7fffffff; /* high |x| */
lx = __LO(x); /* low x */
if((ix|lx)==0) return -1.0/fd_fabs(x);
if(ix>=0x7ff00000) return x*x;
if((ix>>=20)==0) /* IEEE 754 logb */
return -1022.0;
else
return (double) (ix-1023);
}

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@@ -0,0 +1,26 @@
/* @(#)s_matherr.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include "fdlibm.h"
#ifdef __STDC__
int fd_matherr(struct exception *x)
#else
int fd_matherr(x)
struct exception *x;
#endif
{
int n=0;
if(x->arg1!=x->arg1) return 0;
return n;
}

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/* @(#)s_modf.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* modf(double x, double *iptr)
* return fraction part of x, and return x's integral part in *iptr.
* Method:
* Bit twiddling.
*
* Exception:
* No exception.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0;
#else
static double one = 1.0;
#endif
#ifdef __STDC__
double fd_modf(double x, double *iptr)
#else
double fd_modf(x, iptr)
double x,*iptr;
#endif
{
int i0,i1,j0;
unsigned i;
i0 = __HI(x); /* high x */
i1 = __LO(x); /* low x */
j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */
if(j0<20) { /* integer part in high x */
if(j0<0) { /* |x|<1 */
__HIp(iptr) = i0&0x80000000;
__LOp(iptr) = 0; /* *iptr = +-0 */
return x;
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) { /* x is integral */
*iptr = x;
__HI(x) &= 0x80000000;
__LO(x) = 0; /* return +-0 */
return x;
} else {
__HIp(iptr) = i0&(~i);
__LOp(iptr) = 0;
return x - *iptr;
}
}
} else if (j0>51) { /* no fraction part */
*iptr = x*one;
__HI(x) &= 0x80000000;
__LO(x) = 0; /* return +-0 */
return x;
} else { /* fraction part in low x */
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) { /* x is integral */
*iptr = x;
__HI(x) &= 0x80000000;
__LO(x) = 0; /* return +-0 */
return x;
} else {
__HIp(iptr) = i0;
__LOp(iptr) = i1&(~i);
return x - *iptr;
}
}
}

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