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Saxum/extern/bullet/Extras/CDTestFramework/Opcode/Ice/_IceRevisitedRadix.cpp

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Adding Bullet Library
2014-10-24 09:42:47 +00:00
/*
* ICE / OPCODE - Optimized Collision Detection
* http://www.codercorner.com/Opcode.htm
*
* Copyright (c) 2001-2008 Pierre Terdiman, pierre@codercorner.com
This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it freely,
subject to the following restrictions:
1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Contains source code from the article "Radix Sort Revisited".
* \file IceRevisitedRadix.cpp
* \author Pierre Terdiman
* \date April, 4, 2000
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Revisited Radix Sort.
* This is my new radix routine:
* - it uses indices and doesn't recopy the values anymore, hence wasting less ram
* - it creates all the histograms in one run instead of four
* - it sorts words faster than dwords and bytes faster than words
* - it correctly sorts negative floating-point values by patching the offsets
* - it automatically takes advantage of temporal coherence
* - multiple keys support is a side effect of temporal coherence
* - it may be worth recoding in asm... (mainly to use FCOMI, FCMOV, etc) [it's probably memory-bound anyway]
*
* History:
* - 08.15.98: very first version
* - 04.04.00: recoded for the radix article
* - 12.xx.00: code lifting
* - 09.18.01: faster CHECK_PASS_VALIDITY thanks to Mark D. Shattuck (who provided other tips, not included here)
* - 10.11.01: added local ram support
* - 01.20.02: bugfix! In very particular cases the last pass was skipped in the float code-path, leading to incorrect sorting......
* - 01.02.02: - "mIndices" renamed => "mRanks". That's a rank sorter after all.
* - ranks are not "reset" anymore, but implicit on first calls
* - 07.05.02: - offsets rewritten with one less indirection.
* - 11.03.02: - "bool" replaced with RadixHint enum
*
* \class RadixSort
* \author Pierre Terdiman
* \version 1.4
* \date August, 15, 1998
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/*
To do:
- add an offset parameter between two input values (avoid some data recopy sometimes)
- unroll ? asm ?
- 11 bits trick & 3 passes as Michael did
- prefetch stuff the day I have a P3
- make a version with 16-bits indices ?
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Precompiled Header
#include "Stdafx.h"
using namespace IceCore;
#define INVALIDATE_RANKS mCurrentSize|=0x80000000
#define VALIDATE_RANKS mCurrentSize&=0x7fffffff
#define CURRENT_SIZE (mCurrentSize&0x7fffffff)
#define INVALID_RANKS (mCurrentSize&0x80000000)
#define CHECK_RESIZE(n) \
if(n!=mPreviousSize) \
{ \
if(n>mCurrentSize) Resize(n); \
else ResetRanks(); \
mPreviousSize = n; \
}
#define CREATE_HISTOGRAMS(type, buffer) \
/* Clear counters/histograms */ \
ZeroMemory(mHistogram, 256*4*sizeof(udword)); \
\
/* Prepare to count */ \
ubyte* p = (ubyte*)input; \
ubyte* pe = &p[nb*4]; \
udword* h0= &mHistogram[0]; /* Histogram for first pass (LSB) */ \
udword* h1= &mHistogram[256]; /* Histogram for second pass */ \
udword* h2= &mHistogram[512]; /* Histogram for third pass */ \
udword* h3= &mHistogram[768]; /* Histogram for last pass (MSB) */ \
\
bool AlreadySorted = true; /* Optimism... */ \
\
if(INVALID_RANKS) \
{ \
/* Prepare for temporal coherence */ \
type* Running = (type*)buffer; \
type PrevVal = *Running; \
\
while(p!=pe) \
{ \
/* Read input buffer in previous sorted order */ \
type Val = *Running++; \
/* Check whether already sorted or not */ \
if(Val<PrevVal) { AlreadySorted = false; break; } /* Early out */ \
/* Update for next iteration */ \
PrevVal = Val; \
\
/* Create histograms */ \
h0[*p++]++; h1[*p++]++; h2[*p++]++; h3[*p++]++; \
} \
\
/* If all input values are already sorted, we just have to return and leave the */ \
/* previous list unchanged. That way the routine may take advantage of temporal */ \
/* coherence, for example when used to sort transparent faces. */ \
if(AlreadySorted) \
{ \
mNbHits++; \
for(udword i=0;i<nb;i++) mRanks[i] = i; \
return *this; \
} \
} \
else \
{ \
/* Prepare for temporal coherence */ \
udword* Indices = mRanks; \
type PrevVal = (type)buffer[*Indices]; \
\
while(p!=pe) \
{ \
/* Read input buffer in previous sorted order */ \
type Val = (type)buffer[*Indices++]; \
/* Check whether already sorted or not */ \
if(Val<PrevVal) { AlreadySorted = false; break; } /* Early out */ \
/* Update for next iteration */ \
PrevVal = Val; \
\
/* Create histograms */ \
h0[*p++]++; h1[*p++]++; h2[*p++]++; h3[*p++]++; \
} \
\
/* If all input values are already sorted, we just have to return and leave the */ \
/* previous list unchanged. That way the routine may take advantage of temporal */ \
/* coherence, for example when used to sort transparent faces. */ \
if(AlreadySorted) { mNbHits++; return *this; } \
} \
\
/* Else there has been an early out and we must finish computing the histograms */ \
while(p!=pe) \
{ \
/* Create histograms without the previous overhead */ \
h0[*p++]++; h1[*p++]++; h2[*p++]++; h3[*p++]++; \
}
#define CHECK_PASS_VALIDITY(pass) \
/* Shortcut to current counters */ \
udword* CurCount = &mHistogram[pass<<8]; \
\
/* Reset flag. The sorting pass is supposed to be performed. (default) */ \
bool PerformPass = true; \
\
/* Check pass validity */ \
\
/* If all values have the same byte, sorting is useless. */ \
/* It may happen when sorting bytes or words instead of dwords. */ \
/* This routine actually sorts words faster than dwords, and bytes */ \
/* faster than words. Standard running time (O(4*n))is reduced to O(2*n) */ \
/* for words and O(n) for bytes. Running time for floats depends on actual values... */ \
\
/* Get first byte */ \
ubyte UniqueVal = *(((ubyte*)input)+pass); \
\
/* Check that byte's counter */ \
if(CurCount[UniqueVal]==nb) PerformPass=false;
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Constructor.
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
RadixSort::RadixSort() : mRanks(null), mRanks2(null), mCurrentSize(0), mTotalCalls(0), mNbHits(0)
{
#ifndef RADIX_LOCAL_RAM
// Allocate input-independent ram
mHistogram = new udword[256*4];
mOffset = new udword[256];
#endif
// Initialize indices
INVALIDATE_RANKS;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Destructor.
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
RadixSort::~RadixSort()
{
// Release everything
#ifndef RADIX_LOCAL_RAM
DELETEARRAY(mOffset);
DELETEARRAY(mHistogram);
#endif
DELETEARRAY(mRanks2);
DELETEARRAY(mRanks);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Resizes the inner lists.
* \param nb [in] new size (number of dwords)
* \return true if success
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
bool RadixSort::Resize(udword nb)
{
// Free previously used ram
DELETEARRAY(mRanks2);
DELETEARRAY(mRanks);
// Get some fresh one
mRanks = new udword[nb]; CHECKALLOC(mRanks);
mRanks2 = new udword[nb]; CHECKALLOC(mRanks2);
return true;
}
inline_ void RadixSort::CheckResize(udword nb)
{
udword CurSize = CURRENT_SIZE;
if(nb!=CurSize)
{
if(nb>CurSize) Resize(nb);
mCurrentSize = nb;
INVALIDATE_RANKS;
}
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Main sort routine.
* This one is for integer values. After the call, mRanks contains a list of indices in sorted order, i.e. in the order you may process your data.
* \param input [in] a list of integer values to sort
* \param nb [in] number of values to sort, must be < 2^31
* \param hint [in] RADIX_SIGNED to handle negative values, RADIX_UNSIGNED if you know your input buffer only contains positive values
* \return Self-Reference
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
RadixSort& RadixSort::Sort(const udword* input, udword nb, RadixHint hint)
{
// Checkings
if(!input || !nb || nb&0x80000000) return *this;
// Stats
mTotalCalls++;
// Resize lists if needed
CheckResize(nb);
#ifdef RADIX_LOCAL_RAM
// Allocate histograms & offsets on the stack
udword mHistogram[256*4];
// udword mOffset[256];
udword* mLink[256];
#endif
// Create histograms (counters). Counters for all passes are created in one run.
// Pros: read input buffer once instead of four times
// Cons: mHistogram is 4Kb instead of 1Kb
// We must take care of signed/unsigned values for temporal coherence.... I just
// have 2 code paths even if just a single opcode changes. Self-modifying code, someone?
if(hint==RADIX_UNSIGNED) { CREATE_HISTOGRAMS(udword, input); }
else { CREATE_HISTOGRAMS(sdword, input); }
// Compute #negative values involved if needed
udword NbNegativeValues = 0;
if(hint==RADIX_SIGNED)
{
// An efficient way to compute the number of negatives values we'll have to deal with is simply to sum the 128
// last values of the last histogram. Last histogram because that's the one for the Most Significant Byte,
// responsible for the sign. 128 last values because the 128 first ones are related to positive numbers.
udword* h3= &mHistogram[768];
for(udword i=128;i<256;i++) NbNegativeValues += h3[i]; // 768 for last histogram, 128 for negative part
}
// Radix sort, j is the pass number (0=LSB, 3=MSB)
for(udword j=0;j<4;j++)
{
CHECK_PASS_VALIDITY(j);
// Sometimes the fourth (negative) pass is skipped because all numbers are negative and the MSB is 0xFF (for example). This is
// not a problem, numbers are correctly sorted anyway.
if(PerformPass)
{
// Should we care about negative values?
if(j!=3 || hint==RADIX_UNSIGNED)
{
// Here we deal with positive values only
// Create offsets
// mOffset[0] = 0;
// for(udword i=1;i<256;i++) mOffset[i] = mOffset[i-1] + CurCount[i-1];
mLink[0] = mRanks2;
for(udword i=1;i<256;i++) mLink[i] = mLink[i-1] + CurCount[i-1];
}
else
{
// This is a special case to correctly handle negative integers. They're sorted in the right order but at the wrong place.
// Create biased offsets, in order for negative numbers to be sorted as well
// mOffset[0] = NbNegativeValues; // First positive number takes place after the negative ones
mLink[0] = &mRanks2[NbNegativeValues]; // First positive number takes place after the negative ones
// for(udword i=1;i<128;i++) mOffset[i] = mOffset[i-1] + CurCount[i-1]; // 1 to 128 for positive numbers
for(udword i=1;i<128;i++) mLink[i] = mLink[i-1] + CurCount[i-1]; // 1 to 128 for positive numbers
// Fixing the wrong place for negative values
// mOffset[128] = 0;
mLink[128] = mRanks2;
// for(i=129;i<256;i++) mOffset[i] = mOffset[i-1] + CurCount[i-1];
for(udword i=129;i<256;i++) mLink[i] = mLink[i-1] + CurCount[i-1];
}
// Perform Radix Sort
ubyte* InputBytes = (ubyte*)input;
InputBytes += j;
if(INVALID_RANKS)
{
// for(udword i=0;i<nb;i++) mRanks2[mOffset[InputBytes[i<<2]]++] = i;
for(udword i=0;i<nb;i++) *mLink[InputBytes[i<<2]]++ = i;
VALIDATE_RANKS;
}
else
{
udword* Indices = mRanks;
udword* IndicesEnd = &mRanks[nb];
while(Indices!=IndicesEnd)
{
udword id = *Indices++;
// mRanks2[mOffset[InputBytes[id<<2]]++] = id;
*mLink[InputBytes[id<<2]]++ = id;
}
}
// Swap pointers for next pass. Valid indices - the most recent ones - are in mRanks after the swap.
udword* Tmp = mRanks; mRanks = mRanks2; mRanks2 = Tmp;
}
}
return *this;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Main sort routine.
* This one is for floating-point values. After the call, mRanks contains a list of indices in sorted order, i.e. in the order you may process your data.
* \param input [in] a list of floating-point values to sort
* \param nb [in] number of values to sort, must be < 2^31
* \return Self-Reference
* \warning only sorts IEEE floating-point values
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
RadixSort& RadixSort::Sort(const float* input2, udword nb)
{
// Checkings
if(!input2 || !nb || nb&0x80000000) return *this;
// Stats
mTotalCalls++;
udword* input = (udword*)input2;
// Resize lists if needed
CheckResize(nb);
#ifdef RADIX_LOCAL_RAM
// Allocate histograms & offsets on the stack
udword mHistogram[256*4];
// udword mOffset[256];
udword* mLink[256];
#endif
// Create histograms (counters). Counters for all passes are created in one run.
// Pros: read input buffer once instead of four times
// Cons: mHistogram is 4Kb instead of 1Kb
// Floating-point values are always supposed to be signed values, so there's only one code path there.
// Please note the floating point comparison needed for temporal coherence! Although the resulting asm code
// is dreadful, this is surprisingly not such a performance hit - well, I suppose that's a big one on first
// generation Pentiums....We can't make comparison on integer representations because, as Chris said, it just
// wouldn't work with mixed positive/negative values....
{ CREATE_HISTOGRAMS(float, input2); }
// Compute #negative values involved if needed
udword NbNegativeValues = 0;
// An efficient way to compute the number of negatives values we'll have to deal with is simply to sum the 128
// last values of the last histogram. Last histogram because that's the one for the Most Significant Byte,
// responsible for the sign. 128 last values because the 128 first ones are related to positive numbers.
udword* h3= &mHistogram[768];
for(udword i=128;i<256;i++) NbNegativeValues += h3[i]; // 768 for last histogram, 128 for negative part
// Radix sort, j is the pass number (0=LSB, 3=MSB)
for(udword j=0;j<4;j++)
{
// Should we care about negative values?
if(j!=3)
{
// Here we deal with positive values only
CHECK_PASS_VALIDITY(j);
if(PerformPass)
{
// Create offsets
// mOffset[0] = 0;
mLink[0] = mRanks2;
// for(udword i=1;i<256;i++) mOffset[i] = mOffset[i-1] + CurCount[i-1];
for(udword i=1;i<256;i++) mLink[i] = mLink[i-1] + CurCount[i-1];
// Perform Radix Sort
ubyte* InputBytes = (ubyte*)input;
InputBytes += j;
if(INVALID_RANKS)
{
// for(i=0;i<nb;i++) mRanks2[mOffset[InputBytes[i<<2]]++] = i;
for(udword i=0;i<nb;i++) *mLink[InputBytes[i<<2]]++ = i;
VALIDATE_RANKS;
}
else
{
udword* Indices = mRanks;
udword* IndicesEnd = &mRanks[nb];
while(Indices!=IndicesEnd)
{
udword id = *Indices++;
// mRanks2[mOffset[InputBytes[id<<2]]++] = id;
*mLink[InputBytes[id<<2]]++ = id;
}
}
// Swap pointers for next pass. Valid indices - the most recent ones - are in mRanks after the swap.
udword* Tmp = mRanks; mRanks = mRanks2; mRanks2 = Tmp;
}
}
else
{
// This is a special case to correctly handle negative values
CHECK_PASS_VALIDITY(j);
if(PerformPass)
{
// Create biased offsets, in order for negative numbers to be sorted as well
// mOffset[0] = NbNegativeValues; // First positive number takes place after the negative ones
mLink[0] = &mRanks2[NbNegativeValues]; // First positive number takes place after the negative ones
// for(udword i=1;i<128;i++) mOffset[i] = mOffset[i-1] + CurCount[i-1]; // 1 to 128 for positive numbers
for(udword i=1;i<128;i++) mLink[i] = mLink[i-1] + CurCount[i-1]; // 1 to 128 for positive numbers
// We must reverse the sorting order for negative numbers!
// mOffset[255] = 0;
mLink[255] = mRanks2;
// for(i=0;i<127;i++) mOffset[254-i] = mOffset[255-i] + CurCount[255-i]; // Fixing the wrong order for negative values
for(udword i=0;i<127;i++) mLink[254-i] = mLink[255-i] + CurCount[255-i]; // Fixing the wrong order for negative values
// for(i=128;i<256;i++) mOffset[i] += CurCount[i]; // Fixing the wrong place for negative values
for(udword i=128;i<256;i++) mLink[i] += CurCount[i]; // Fixing the wrong place for negative values
// Perform Radix Sort
if(INVALID_RANKS)
{
for(udword i=0;i<nb;i++)
{
udword Radix = input[i]>>24; // Radix byte, same as above. AND is useless here (udword).
// ### cmp to be killed. Not good. Later.
// if(Radix<128) mRanks2[mOffset[Radix]++] = i; // Number is positive, same as above
// else mRanks2[--mOffset[Radix]] = i; // Number is negative, flip the sorting order
if(Radix<128) *mLink[Radix]++ = i; // Number is positive, same as above
else *(--mLink[Radix]) = i; // Number is negative, flip the sorting order
}
VALIDATE_RANKS;
}
else
{
for(udword i=0;i<nb;i++)
{
udword Radix = input[mRanks[i]]>>24; // Radix byte, same as above. AND is useless here (udword).
// ### cmp to be killed. Not good. Later.
// if(Radix<128) mRanks2[mOffset[Radix]++] = mRanks[i]; // Number is positive, same as above
// else mRanks2[--mOffset[Radix]] = mRanks[i]; // Number is negative, flip the sorting order
if(Radix<128) *mLink[Radix]++ = mRanks[i]; // Number is positive, same as above
else *(--mLink[Radix]) = mRanks[i]; // Number is negative, flip the sorting order
}
}
// Swap pointers for next pass. Valid indices - the most recent ones - are in mRanks after the swap.
udword* Tmp = mRanks; mRanks = mRanks2; mRanks2 = Tmp;
}
else
{
// The pass is useless, yet we still have to reverse the order of current list if all values are negative.
if(UniqueVal>=128)
{
if(INVALID_RANKS)
{
// ###Possible?
for(udword i=0;i<nb;i++) mRanks2[i] = nb-i-1;
VALIDATE_RANKS;
}
else
{
for(udword i=0;i<nb;i++) mRanks2[i] = mRanks[nb-i-1];
}
// Swap pointers for next pass. Valid indices - the most recent ones - are in mRanks after the swap.
udword* Tmp = mRanks; mRanks = mRanks2; mRanks2 = Tmp;
}
}
}
}
return *this;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
* Gets the ram used.
* \return memory used in bytes
*/
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
udword RadixSort::GetUsedRam() const
{
udword UsedRam = sizeof(RadixSort);
#ifndef RADIX_LOCAL_RAM
UsedRam += 256*4*sizeof(udword); // Histograms
UsedRam += 256*sizeof(udword); // Offsets
#endif
UsedRam += 2*CURRENT_SIZE*sizeof(udword); // 2 lists of indices
return UsedRam;
}
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