---

blocksort.c

Go to the documentation of this file.

/*-------------------------------------------------------------*/
/*--- Block sorting machinery                               ---*/
/*---                                           blocksort.c ---*/
/*-------------------------------------------------------------*/

/*--
  This file is a part of bzip2 and/or libbzip2, a program and
  library for lossless, block-sorting data compression.

  Copyright (C) 1996-1999 Julian R Seward.  All rights reserved.

  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions
  are met:

  1. Redistributions of source code must retain the above copyright
     notice, this list of conditions and the following disclaimer.

  2. 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.

  3. Altered source versions must be plainly marked as such, and must
     not be misrepresented as being the original software.

  4. The name of the author may not be used to endorse or promote 
     products derived from this software without specific prior written 
     permission.

  THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
  OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
  DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
  GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
  WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

  Julian Seward, Cambridge, UK.
  jseward@acm.org
  bzip2/libbzip2 version 0.9.5 of 24 May 1999

  This program is based on (at least) the work of:
     Mike Burrows
     David Wheeler
     Peter Fenwick
     Alistair Moffat
     Radford Neal
     Ian H. Witten
     Robert Sedgewick
     Jon L. Bentley

  For more information on these sources, see the manual.
--*/


#include "bzlib_private.h"

/*---------------------------------------------*/
/*--- Fallback O(N log(N)^2) sorting        ---*/
/*--- algorithm, for repetitive blocks      ---*/
/*---------------------------------------------*/

/*---------------------------------------------*/
static 
__inline__
void fallbackSimpleSort ( UInt32* fmap, 
                          UInt32* eclass, 
                          Int32   lo, 
                          Int32   hi )
{
   Int32 i, j, tmp;
   UInt32 ec_tmp;

   if (lo == hi) return;

   if (hi - lo > 3) {
      for ( i = hi-4; i >= lo; i-- ) {
         tmp = fmap[i];
         ec_tmp = eclass[tmp];
         for ( j = i+4; j <= hi && ec_tmp > eclass[fmap[j]]; j += 4 )
            fmap[j-4] = fmap[j];
         fmap[j-4] = tmp;
      }
   }

   for ( i = hi-1; i >= lo; i-- ) {
      tmp = fmap[i];
      ec_tmp = eclass[tmp];
      for ( j = i+1; j <= hi && ec_tmp > eclass[fmap[j]]; j++ )
         fmap[j-1] = fmap[j];
      fmap[j-1] = tmp;
   }
}


/*---------------------------------------------*/
#define fswap(zz1, zz2) \
   { Int32 zztmp = zz1; zz1 = zz2; zz2 = zztmp; }

#define fvswap(zzp1, zzp2, zzn)       \
{                                     \
   Int32 yyp1 = (zzp1);               \
   Int32 yyp2 = (zzp2);               \
   Int32 yyn  = (zzn);                \
   while (yyn > 0) {                  \
      fswap(fmap[yyp1], fmap[yyp2]);  \
      yyp1++; yyp2++; yyn--;          \
   }                                  \
}


#define fmin(a,b) ((a) < (b)) ? (a) : (b)

#define fpush(lz,hz) { stackLo[sp] = lz; \
                       stackHi[sp] = hz; \
                       sp++; }

#define fpop(lz,hz) { sp--;              \
                      lz = stackLo[sp];  \
                      hz = stackHi[sp]; }

#define FALLBACK_QSORT_SMALL_THRESH 10
#define FALLBACK_QSORT_STACK_SIZE   100


static
void fallbackQSort3 ( UInt32* fmap, 
                      UInt32* eclass,
                      Int32   loSt, 
                      Int32   hiSt )
{
   Int32 unLo, unHi, ltLo, gtHi, n, m;
   Int32 sp, lo, hi;
   UInt32 med, r, r3;
   Int32 stackLo[FALLBACK_QSORT_STACK_SIZE];
   Int32 stackHi[FALLBACK_QSORT_STACK_SIZE];

   r = 0;

   sp = 0;
   fpush ( loSt, hiSt );

   while (sp > 0) {

      AssertH ( sp < FALLBACK_QSORT_STACK_SIZE, 1004 );

      fpop ( lo, hi );
      if (hi - lo < FALLBACK_QSORT_SMALL_THRESH) {
         fallbackSimpleSort ( fmap, eclass, lo, hi );
         continue;
      }

      /* Random partitioning.  Median of 3 sometimes fails to
         avoid bad cases.  Median of 9 seems to help but 
         looks rather expensive.  This too seems to work but
         is cheaper.  Guidance for the magic constants 
         7621 and 32768 is taken from Sedgewick's algorithms
         book, chapter 35.
      */
      r = ((r * 7621) + 1) % 32768;
      r3 = r % 3;
      if (r3 == 0) med = eclass[fmap[lo]]; else
      if (r3 == 1) med = eclass[fmap[(lo+hi)>>1]]; else
                   med = eclass[fmap[hi]];

      unLo = ltLo = lo;
      unHi = gtHi = hi;

      while (1) {
         while (1) {
            if (unLo > unHi) break;
            n = (Int32)eclass[fmap[unLo]] - (Int32)med;
            if (n == 0) { 
               fswap(fmap[unLo], fmap[ltLo]); 
               ltLo++; unLo++; 
               continue; 
            };
            if (n > 0) break;
            unLo++;
         }
         while (1) {
            if (unLo > unHi) break;
            n = eclass[fmap[unHi]] - med;
            if (n == 0) { 
               fswap(fmap[unHi], fmap[gtHi]); 
               gtHi--; unHi--; 
               continue; 
            };
            if (n < 0) break;
            unHi--;
         }
         if (unLo > unHi) break;
         fswap(fmap[unLo], fmap[unHi]); unLo++; unHi--;
      }

      AssertD ( unHi == unLo-1, "fallbackQSort3(2)" );

      if (gtHi < ltLo) continue;

      n = fmin(ltLo-lo, unLo-ltLo); fvswap(lo, unLo-n, n);
      m = fmin(hi-gtHi, gtHi-unHi); fvswap(unLo, hi-m+1, m);

      n = lo + unLo - ltLo - 1;
      m = hi - (gtHi - unHi) + 1;

      if (n - lo > hi - m) {
         fpush ( lo, n );
         fpush ( m, hi );
      } else {
         fpush ( m, hi );
         fpush ( lo, n );
      }
   }
}

#undef fmin
#undef fpush
#undef fpop
#undef fswap
#undef fvswap
#undef FALLBACK_QSORT_SMALL_THRESH
#undef FALLBACK_QSORT_STACK_SIZE


/*---------------------------------------------*/
/* Pre:
      nblock > 0
      eclass exists for [0 .. nblock-1]
      ((UInt16*)eclass) [0 .. nblock-1] [15:8] holds block
      ptr exists for [0 .. nblock-1]

   Post:
      ((UInt16*)eclass) [0 .. nblock-1] [15:8] holds block
      All other areas of eclass destroyed
      fmap [0 .. nblock-1] holds sorted order
      bhtab [ 0 .. 2+(nblock/32) ] destroyed
*/

#define       SET_BH(zz)  bhtab[(zz) >> 5] |= (1 << ((zz) & 31))
#define     CLEAR_BH(zz)  bhtab[(zz) >> 5] &= ~(1 << ((zz) & 31))
#define     ISSET_BH(zz)  (bhtab[(zz) >> 5] & (1 << ((zz) & 31)))
#define      WORD_BH(zz)  bhtab[(zz) >> 5]
#define UNALIGNED_BH(zz)  ((zz) & 0x01f)

static
void fallbackSort ( UInt32* fmap, 
                    UInt32* eclass, 
                    UInt32* bhtab,
                    Int32   nblock,
                    Int32   verb )
{
   Int32 ftab[257];
   Int32 ftabCopy[256];
   Int32 H, i, j, k, l, r, cc, cc1;
   Int32 nNotDone;
   Int32 nBhtab;
   UInt16* eclass16 = (UInt16*)eclass;

   /*--
      Initial 1-char radix sort to generate
      initial fmap and initial BH bits.
   --*/
   if (verb >= 4)
      VPrintf0 ( "        bucket sorting ...\n" );
   for (i = 0; i < 257;    i++) ftab[i] = 0;
   for (i = 0; i < nblock; i++) ftab[eclass16[i] >> 8]++;
   for (i = 0; i < 256;    i++) ftabCopy[i] = ftab[i];
   for (i = 1; i < 257;    i++) ftab[i] += ftab[i-1];

   for (i = 0; i < nblock; i++) {
      j = eclass16[i] >> 8;
      k = ftab[j] - 1;
      ftab[j] = k;
      fmap[k] = i;
   }

   nBhtab = 2 + (nblock / 32);
   for (i = 0; i < nBhtab; i++) bhtab[i] = 0;
   for (i = 0; i < 256; i++) SET_BH(ftab[i]);

   /*--
      Inductively refine the buckets.  Kind-of an
      "exponential radix sort" (!), inspired by the
      Manber-Myers suffix array construction algorithm.
   --*/

   /*-- set sentinel bits for block-end detection --*/
   for (i = 0; i < 32; i++) { 
      SET_BH(nblock + 2*i);
      CLEAR_BH(nblock + 2*i + 1);
   }

   /*-- the log(N) loop --*/
   H = 1;
   while (1) {

      if (verb >= 4) 
         VPrintf1 ( "        depth %6d has ", H );

      j = 0;
      for (i = 0; i < nblock; i++) {
         if (ISSET_BH(i)) j = i;
         k = fmap[i] - H; if (k < 0) k += nblock;
         eclass[k] = j;
      }

      nNotDone = 0;
      r = -1;
      while (1) {

         /*-- find the next non-singleton bucket --*/
         k = r + 1;
         while (ISSET_BH(k) && UNALIGNED_BH(k)) k++;
         if (ISSET_BH(k)) {
            while (WORD_BH(k) == 0xffffffff) k += 32;
            while (ISSET_BH(k)) k++;
         }
         l = k - 1;
         if (l >= nblock) break;
         while (!ISSET_BH(k) && UNALIGNED_BH(k)) k++;
         if (!ISSET_BH(k)) {
            while (WORD_BH(k) == 0x00000000) k += 32;
            while (!ISSET_BH(k)) k++;
         }
         r = k - 1;
         if (r >= nblock) break;

         /*-- now [l, r] bracket current bucket --*/
         if (r > l) {
            nNotDone += (r - l + 1);
            fallbackQSort3 ( fmap, eclass, l, r );

            /*-- scan bucket and generate header bits-- */
            cc = -1;
            for (i = l; i <= r; i++) {
               cc1 = eclass[fmap[i]];
               if (cc != cc1) { SET_BH(i); cc = cc1; };
            }
         }
      }

      if (verb >= 4) 
         VPrintf1 ( "%6d unresolved strings\n", nNotDone );

      H *= 2;
      if (H > nblock || nNotDone == 0) break;
   }

   /*-- 
      Reconstruct the original block in
      eclass16 [0 .. nblock-1] [15:8], since the
      previous phase destroyed it.
   --*/
   if (verb >= 4)
      VPrintf0 ( "        reconstructing block ...\n" );
   j = 0;
   for (i = 0; i < nblock; i++) {
      while (ftabCopy[j] == 0) j++;
      ftabCopy[j]--;
      eclass16[fmap[i]] = j << 8;
   }
   AssertH ( j < 256, 1005 );
}

#undef       SET_BH
#undef     CLEAR_BH
#undef     ISSET_BH
#undef      WORD_BH
#undef UNALIGNED_BH


/*---------------------------------------------*/
/*--- The main, O(N^2 log(N)) sorting       ---*/
/*--- algorithm.  Faster for "normal"       ---*/
/*--- non-repetitive blocks.                ---*/
/*---------------------------------------------*/

/*---------------------------------------------*/
static
__inline__
Bool mainGtU ( UInt32  i1, 
               UInt32  i2,
               UInt16* block, 
               UInt16* quadrant,
               UInt32  nblock,
               Int32*  budget )
{
   Int32 k;
   UInt16 s1, s2;

   AssertD ( i1 != i2, "mainGtU" );

   s1 = block[i1]; s2 = block[i2];
   if (s1 != s2) return (s1 > s2);
   i1 += 2; i2 += 2;

   s1 = block[i1]; s2 = block[i2];
   if (s1 != s2) return (s1 > s2);
   i1 += 2; i2 += 2;

   s1 = block[i1]; s2 = block[i2];
   if (s1 != s2) return (s1 > s2);
   i1 += 2; i2 += 2;

   s1 = block[i1]; s2 = block[i2];
   if (s1 != s2) return (s1 > s2);
   i1 += 2; i2 += 2;

   s1 = block[i1]; s2 = block[i2];
   if (s1 != s2) return (s1 > s2);
   i1 += 2; i2 += 2;

   s1 = block[i1]; s2 = block[i2];
   if (s1 != s2) return (s1 > s2);
   i1 += 2; i2 += 2;

   k = nblock + 8;

   do {

      s1 = block[i1]; s2 = block[i2];
      if (s1 != s2) return (s1 > s2);
      s1 = quadrant[i1]; s2 = quadrant[i2];
      if (s1 != s2) return (s1 > s2);
      i1 += 2; i2 += 2;

      s1 = block[i1]; s2 = block[i2];
      if (s1 != s2) return (s1 > s2);
      s1 = quadrant[i1]; s2 = quadrant[i2];
      if (s1 != s2) return (s1 > s2);
      i1 += 2; i2 += 2;

      s1 = block[i1]; s2 = block[i2];
      if (s1 != s2) return (s1 > s2);
      s1 = quadrant[i1]; s2 = quadrant[i2];
      if (s1 != s2) return (s1 > s2);
      i1 += 2; i2 += 2;

      s1 = block[i1]; s2 = block[i2];
      if (s1 != s2) return (s1 > s2);
      s1 = quadrant[i1]; s2 = quadrant[i2];
      if (s1 != s2) return (s1 > s2);
      i1 += 2; i2 += 2;

      if (i1 >= nblock) i1 -= nblock;
      if (i2 >= nblock) i2 -= nblock;

      k -= 8;
      (*budget)--;
   }
      while (k >= 0);

   return False;
}


/*---------------------------------------------*/
/*--
   Knuth's increments seem to work better
   than Incerpi-Sedgewick here.  Possibly
   because the number of elems to sort is
   usually small, typically <= 20.
--*/
Int32 incs[14] = { 1, 4, 13, 40, 121, 364, 1093, 3280,
                   9841, 29524, 88573, 265720,
                   797161, 2391484 };

static
void mainSimpleSort ( UInt32* ptr,
                      UInt16* block,
                      UInt16* quadrant,
                      Int32   nblock,
                      Int32   lo, 
                      Int32   hi, 
                      Int32   d,
                      Int32*  budget )
{
   Int32 i, j, h, bigN, hp;
   UInt32 v;

   bigN = hi - lo + 1;
   if (bigN < 2) return;

   hp = 0;
   while (incs[hp] < bigN) hp++;
   hp--;

   for (; hp >= 0; hp--) {
      h = incs[hp];

      i = lo + h;
      while (True) {

         /*-- copy 1 --*/
         if (i > hi) break;
         v = ptr[i];
         j = i;
         while ( mainGtU ( 
                    ptr[j-h]+d, v+d, block, quadrant, nblock, budget 
                 ) ) {
            ptr[j] = ptr[j-h];
            j = j - h;
            if (j <= (lo + h - 1)) break;
         }
         ptr[j] = v;
         i++;

         /*-- copy 2 --*/
         if (i > hi) break;
         v = ptr[i];
         j = i;
         while ( mainGtU ( 
                    ptr[j-h]+d, v+d, block, quadrant, nblock, budget 
                 ) ) {
            ptr[j] = ptr[j-h];
            j = j - h;
            if (j <= (lo + h - 1)) break;
         }
         ptr[j] = v;
         i++;

         /*-- copy 3 --*/
         if (i > hi) break;
         v = ptr[i];
         j = i;
         while ( mainGtU ( 
                    ptr[j-h]+d, v+d, block, quadrant, nblock, budget 
                 ) ) {
            ptr[j] = ptr[j-h];
            j = j - h;
            if (j <= (lo + h - 1)) break;
         }
         ptr[j] = v;
         i++;

         if (*budget < 0) return;
      }
   }
}


/*---------------------------------------------*/
/*--
   The following is an implementation of
   an elegant 3-way quicksort for strings,
   described in a paper "Fast Algorithms for
   Sorting and Searching Strings", by Robert
   Sedgewick and Jon L. Bentley.
--*/

#define mswap(zz1, zz2) \
   { Int32 zztmp = zz1; zz1 = zz2; zz2 = zztmp; }

#define mvswap(zzp1, zzp2, zzn)       \
{                                     \
   Int32 yyp1 = (zzp1);               \
   Int32 yyp2 = (zzp2);               \
   Int32 yyn  = (zzn);                \
   while (yyn > 0) {                  \
      mswap(ptr[yyp1], ptr[yyp2]);    \
      yyp1++; yyp2++; yyn--;          \
   }                                  \
}


static 
__inline__
UInt16 mmed3 ( UInt16 a, UInt16 b, UInt16 c )
{
   UInt16 t;
   if (a > b) { t = a; a = b; b = t; };
   if (b > c) { t = b; b = c; c = t; };
   if (a > b)          b = a;
   return b;
}


#define mmin(a,b) ((a) < (b)) ? (a) : (b)

#define mpush(lz,hz,dz) { stackLo[sp] = lz; \
                          stackHi[sp] = hz; \
                          stackD [sp] = dz; \
                          sp++; }

#define mpop(lz,hz,dz) { sp--;             \
                         lz = stackLo[sp]; \
                         hz = stackHi[sp]; \
                         dz = stackD [sp]; }


#define mnextsize(az) (nextHi[az]-nextLo[az])

#define mnextswap(az,bz)                                        \
   { Int32 tz;                                                  \
     tz = nextLo[az]; nextLo[az] = nextLo[bz]; nextLo[bz] = tz; \
     tz = nextHi[az]; nextHi[az] = nextHi[bz]; nextHi[bz] = tz; \
     tz = nextD [az]; nextD [az] = nextD [bz]; nextD [bz] = tz; }


#define MAIN_QSORT_SMALL_THRESH 20
#define MAIN_QSORT_DEPTH_THRESH (BZ_N_RADIX + BZ_N_QSORT)
#define MAIN_QSORT_STACK_SIZE 100

static
void mainQSort3 ( UInt32* ptr,
                  UInt16* block,
                  UInt16* quadrant,
                  Int32   nblock,
                  Int32   loSt, 
                  Int32   hiSt, 
                  Int32   dSt,
                  Int32*  budget )
{
   Int32 unLo, unHi, ltLo, gtHi, n, m, med;
   Int32 sp, lo, hi, d;

   Int32 stackLo[MAIN_QSORT_STACK_SIZE];
   Int32 stackHi[MAIN_QSORT_STACK_SIZE];
   Int32 stackD [MAIN_QSORT_STACK_SIZE];

   Int32 nextLo[3];
   Int32 nextHi[3];
   Int32 nextD [3];

   sp = 0;
   mpush ( loSt, hiSt, dSt );

   while (sp > 0) {

      AssertH ( sp < MAIN_QSORT_STACK_SIZE, 1001 );

      mpop ( lo, hi, d );
      if (hi - lo < MAIN_QSORT_SMALL_THRESH || 
          d > MAIN_QSORT_DEPTH_THRESH) {
         mainSimpleSort ( ptr, block, quadrant, nblock, lo, hi, d, budget );
         if (*budget < 0) return;
         continue;
      }

      med = (Int32) 
            mmed3 ( block[ptr[ lo         ]+d],
                    block[ptr[ hi         ]+d],
                    block[ptr[ (lo+hi)>>1 ]+d] );

      unLo = ltLo = lo;
      unHi = gtHi = hi;

      while (True) {
         while (True) {
            if (unLo > unHi) break;
            n = ((Int32)block[ptr[unLo]+d]) - med;
            if (n == 0) { 
               mswap(ptr[unLo], ptr[ltLo]); 
               ltLo++; unLo++; continue; 
            };
            if (n >  0) break;
            unLo++;
         }
         while (True) {
            if (unLo > unHi) break;
            n = ((Int32)block[ptr[unHi]+d]) - med;
            if (n == 0) { 
               mswap(ptr[unHi], ptr[gtHi]); 
               gtHi--; unHi--; continue; 
            };
            if (n <  0) break;
            unHi--;
         }
         if (unLo > unHi) break;
         mswap(ptr[unLo], ptr[unHi]); unLo++; unHi--;
      }

      AssertD ( unHi == unLo-1, "mainQSort3(2)" );

      if (gtHi < ltLo) {
         mpush(lo, hi, d+2 );
         continue;
      }

      n = mmin(ltLo-lo, unLo-ltLo); mvswap(lo, unLo-n, n);
      m = mmin(hi-gtHi, gtHi-unHi); mvswap(unLo, hi-m+1, m);

      n = lo + unLo - ltLo - 1;
      m = hi - (gtHi - unHi) + 1;

      nextLo[0] = lo;  nextHi[0] = n;   nextD[0] = d;
      nextLo[1] = m;   nextHi[1] = hi;  nextD[1] = d;
      nextLo[2] = n+1; nextHi[2] = m-1; nextD[2] = d+2;

      if (mnextsize(0) < mnextsize(1)) mnextswap(0,1);
      if (mnextsize(1) < mnextsize(2)) mnextswap(1,2);
      if (mnextsize(0) < mnextsize(1)) mnextswap(0,1);

      AssertD (mnextsize(0) >= mnextsize(1), "mainQSort3(8)" );
      AssertD (mnextsize(1) >= mnextsize(2), "mainQSort3(9)" );

      mpush (nextLo[0], nextHi[0], nextD[0]);
      mpush (nextLo[1], nextHi[1], nextD[1]);
      mpush (nextLo[2], nextHi[2], nextD[2]);
   }
}

#undef mswap
#undef mvswap
#undef mpush
#undef mpop
#undef mmin
#undef mnextsize
#undef mnextswap
#undef MAIN_QSORT_SMALL_THRESH
#undef MAIN_QSORT_DEPTH_THRESH
#undef MAIN_QSORT_STACK_SIZE


/*---------------------------------------------*/
/* Pre:
      nblock > N_OVERSHOOT
      block32 exists for [0 .. nblock-1 +N_OVERSHOOT]
      ((UInt16*)block32) [0 .. nblock-1] [15:8] holds block
      ptr exists for [0 .. nblock-1]

   Post:
      ((UInt16*)block32) [0 .. nblock-1] [15:8] holds block
      All other areas of block32 destroyed
      ftab [0 .. 65536 ] destroyed
      ptr [0 .. nblock-1] holds sorted order
      if (*budget < 0), sorting was abandoned
*/

#define BIGFREQ(b) (ftab[((b)+1) << 8] - ftab[(b) << 8])
#define SETMASK (1 << 21)
#define CLEARMASK (~(SETMASK))

static
void mainSort ( UInt32* ptr, 
                UInt16* block,
                UInt16* quadrant, 
                UInt32* ftab,
                Int32   nblock,
                Int32   verb,
                Int32*  budget )
{
   Int32  i, j, k, m, ss, sb;
   Int32  runningOrder[256];
   Int32  copy[256];
   Bool   bigDone[256];
   UChar  c1;
   Int32  numQSorted;
   Int32  biggestSoFar;
   UInt16 s;

   if (verb >= 4) VPrintf0 ( "        main sort initialise ...\n" );

   /*-- Stripe the block data into 16 bits, and at the
        same time set up the 2-byte frequency table 
   --*/
   for (i = 65536; i >= 0; i--) ftab[i] = 0;

   s = block[0];
   for (i = 1; i < nblock; i++) {
      quadrant[i] = 0;
      s = (s << 8) | block[i];
      block[i-1] = s;
      ftab[s]++;      
   }
   quadrant[0] = 0;
   s = (s << 8) | (block[0] >> 8);
   block[nblock-1] = s;
   ftab[s]++;

   /*-- (emphasises close relationship of block & quadrant) --*/
   for (i = 0; i < BZ_N_OVERSHOOT; i++) {
      block   [nblock+i] = block[i];
      quadrant[nblock+i] = 0;
   }

   if (verb >= 4) VPrintf0 ( "        bucket sorting ...\n" );

   /*-- Complete the initial radix sort --*/
   for (i = 1; i <= 65536; i++) ftab[i] += ftab[i-1];

   for (i = 0; i < nblock; i++) {
      s = block[i];
      j = ftab[s] - 1;
      ftab[s] = j;
      ptr[j] = i;
   }

   /*--
      Now ftab contains the first loc of every small bucket.
      Calculate the running order, from smallest to largest
      big bucket.
   --*/
   for (i = 0; i <= 255; i++) {
      bigDone     [i] = False;
      runningOrder[i] = i;
   }

   {
      Int32 vv;
      Int32 h = 1;
      do h = 3 * h + 1; while (h <= 256);
      do 
                {
//                      printf("h=%lu\n",h);
         h = h / 3;
         for (i = h; i <= 255; i++) 
                        {
//                              printf("i=%lu\n",i);
            vv = runningOrder[i];
            j = i;
            while ( BIGFREQ(runningOrder[j-h]) > BIGFREQ(vv) ) {
//                                              printf("j=%lu\n",j);
                                                j-=h;
               runningOrder[j+h] = runningOrder[j];
//                                      printf("j-h=%lu\n",j-h);
//               j = j - h;

//                                      printf("j=%lu\n",j);
               if (j <= (h - 1)) goto zero;
            }
            zero:
            runningOrder[j] = vv;
         }
      } while (h != 1);
   }

   /*--
      The main sorting loop.
   --*/

   biggestSoFar = numQSorted = 0;

   for (i = 0; i <= 255; i++) {

      /*--
         Process big buckets, starting with the least full.
         Basically this is a 4-step process in which we call
         mainQSort3 to sort the small buckets [ss, j], but
         also make a big effort to avoid the calls if we can.
      --*/
      ss = runningOrder[i];

      /*--
         Step 1:
         Complete the big bucket [ss] by quicksorting
         any unsorted small buckets [ss, j], for j != ss.  
         Hopefully previous pointer-scanning phases have already
         completed many of the small buckets [ss, j], so
         we don't have to sort them at all.
      --*/
      for (j = 0; j <= 255; j++) {
         if (j != ss) {
            sb = (ss << 8) + j;
            if ( ! (ftab[sb] & SETMASK) ) {
               Int32 lo = ftab[sb]   & CLEARMASK;
               Int32 hi = (ftab[sb+1] & CLEARMASK) - 1;
               if (hi > lo) {
                  if (verb >= 4)
                     VPrintf4 ( "        qsort [0x%x, 0x%x]   "
                                "done %d   this %d\n",
                                ss, j, numQSorted, hi - lo + 1 );
                  mainQSort3 ( 
                     ptr, block, quadrant, nblock, 
                     lo, hi, BZ_N_RADIX, budget 
                  );   
                  numQSorted += (hi - lo + 1);
                  if (*budget < 0) return;
               }
            }
            ftab[sb] |= SETMASK;
         }
      }

      /*--
         Step 2:
         Deal specially with case [ss, ss].  This establishes the
         sorted order for [ss, ss] without any comparisons.  
         A clever trick, cryptically described as steps Q6b and Q6c
         in SRC-124 (aka BW94).  Compared to bzip2, this makes it
         practical not to use a preliminary run-length coder.
      --*/
      {
         Int32 put0, get0, put1, get1;
         Int32 sbn = (ss << 8) + ss;
         Int32 lo = ftab[sbn] & CLEARMASK;
         Int32 hi = (ftab[sbn+1] & CLEARMASK) - 1;
         UChar ssc = (UChar)ss;
         put0 = lo;
         get0 = ftab[ss << 8] & CLEARMASK;
         put1 = hi;
         get1 = (ftab[(ss+1) << 8] & CLEARMASK) - 1;
         while (get0 < put0) {
            j = ptr[get0]-1; if (j < 0) j += nblock;
            c1 = (UChar)(block[j] >> 8);
            if (c1 == ssc) { ptr[put0] = j; put0++; };
            get0++;
         }
         while (get1 > put1) {
            j = ptr[get1]-1; if (j < 0) j += nblock;
            c1 = (UChar)(block[j] >> 8);
            if (c1 == ssc) { ptr[put1] = j; put1--; };
            get1--;
         }
         ftab[sbn] |= SETMASK;
      }

      /*--
         Step 3:
         The [ss] big bucket is now done.  Record this fact,
         and update the quadrant descriptors.  Remember to
         update quadrants in the overshoot area too, if
         necessary.  The "if (i < 255)" test merely skips
         this updating for the last bucket processed, since
         updating for the last bucket is pointless.

         The quadrant array provides a way to incrementally
         cache sort orderings, as they appear, so as to 
         make subsequent comparisons in fullGtU() complete
         faster.  For repetitive blocks this makes a big
         difference (but not big enough to be able to avoid
         the fallback sorting mechanism, exponential radix sort).

         The precise meaning is: at all times:

            for 0 <= i < nblock and 0 <= j <= nblock

            if block[i] != block[j], 

               then the relative values of quadrant[i] and 
                    quadrant[j] are meaningless.

               else {
                  if quadrant[i] < quadrant[j]
                     then the string starting at i lexicographically
                     precedes the string starting at j

                  else if quadrant[i] > quadrant[j]
                     then the string starting at j lexicographically
                     precedes the string starting at i

                  else
                     the relative ordering of the strings starting
                     at i and j has not yet been determined.
               }
      --*/
      bigDone[ss] = True;

      if (i < 255) {
         Int32 bbStart  = ftab[ss << 8] & CLEARMASK;
         Int32 bbSize   = (ftab[(ss+1) << 8] & CLEARMASK) - bbStart;
         Int32 shifts   = 0;

         while ((bbSize >> shifts) > 65534) shifts++;

         for (j = 0; j < bbSize; j++) {
            Int32 a2update     = ptr[bbStart + j];
            UInt16 qVal        = (UInt16)(j >> shifts);
            quadrant[a2update] = qVal;
            if (a2update < BZ_N_OVERSHOOT)
               quadrant[a2update + nblock] = qVal;
         }
         AssertH ( ((bbSize-1) >> shifts) <= 65535, 1002 );
      }

      /*--
         Step 4:
         Now scan this big bucket [ss] so as to synthesise the
         sorted order for small buckets [t, ss] for all t != ss.
         This will avoid doing Real Work in subsequent Step 1's.
      --*/
      for (j = 0; j <= 255; j++)
         copy[j] = ftab[(j << 8) + ss] & CLEARMASK;

      m = ftab[(ss+1) << 8] & CLEARMASK;
      for (j = ftab[ss << 8] & CLEARMASK; j < m; j++) {
         k = ptr[j] - 1; if (k < 0) k += nblock;
         c1 = (UChar)(block[k] >> 8);
         if ( ! bigDone[c1] ) {
            ptr[copy[c1]] = k;
            copy[c1] ++;
         }
      }

      for (j = 0; j <= 255; j++) ftab[(j << 8) + ss] |= SETMASK;
   }

   if (verb >= 4)
      VPrintf3 ( "        %d pointers, %d sorted, %d scanned\n",
                 nblock, numQSorted, nblock - numQSorted );
}

#undef BIGFREQ
#undef SETMASK
#undef CLEARMASK


/*---------------------------------------------*/
/* Pre:
      nblock > 0
      arr2 exists for [0 .. nblock-1 +N_OVERSHOOT]
      ((UInt16*)arr2) [0 .. nblock-1] [15:8] holds block
      arr1 exists for [0 .. nblock-1]

   Post:
      ((UInt16*)arr2) [0 .. nblock-1] [15:8] holds block
      All other areas of block destroyed
      ftab [ 0 .. 65536 ] destroyed
      arr1 [0 .. nblock-1] holds sorted order
*/
void blockSort ( EState* s )
{
   UInt32* ptr    = s->ptr; 
   UInt16* block  = s->block;
   UInt32* ftab   = s->ftab;
   Int32   nblock = s->nblock;
   Int32   verb   = s->verbosity;
   Int32   wfact  = s->workFactor;
   UInt16* quadrant;
   Int32   budget;
   Int32   budgetInit;
   Int32   i;

   if (nblock < 10000) {
      for (i = 0; i < nblock; i++) block[i] <<= 8;
      fallbackSort ( s->arr1, s->arr2, ftab, nblock, verb );
   } else {
      quadrant = &(block[nblock+BZ_N_OVERSHOOT]);

      /* (wfact-1) / 3 puts the default-factor-30
         transition point at very roughly the same place as 
         with v0.1 and v0.9.0.  
         Not that it particularly matters any more, since the
         resulting compressed stream is now the same regardless
         of whether or not we use the main sort or fallback sort.
      */
      if (wfact < 1  ) wfact = 1;
      if (wfact > 100) wfact = 100;
      budgetInit = nblock * ((wfact-1) / 3);
      budget = budgetInit;

      mainSort ( ptr, block, quadrant, ftab, nblock, verb, &budget );
      if (verb >= 3) 
         VPrintf3 ( "      %d work, %d block, ratio %5.2f\n",
                    budgetInit - budget,
                    nblock, 
                    (float)(budgetInit - budget) /
                    (float)(nblock==0 ? 1 : nblock) ); 
      if (budget < 0) {
         if (verb >= 2) 
            VPrintf0 ( "    too repetitive; using fallback"
                       " sorting algorithm\n" );
         fallbackSort ( s->arr1, s->arr2, ftab, nblock, verb );
      }
   }

   s->origPtr = -1;
   for (i = 0; i < s->nblock; i++)
      if (ptr[i] == 0)
         { s->origPtr = i; break; };

   AssertH( s->origPtr != -1, 1003 );
}


/*-------------------------------------------------------------*/
/*--- end                                       blocksort.c ---*/
/*-------------------------------------------------------------*/

---