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+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+/**
+ * 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() : mCurrentSize(0), mRanks(null), mRanks2(null), 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;
+}