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