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jrevdct.cpp

/*
 * jrevdct.c
 *
 * This file is part of the Independent JPEG Group's software.
 * The IJG code is distributed under the terms reproduced here:
 * 
 * LEGAL ISSUES
 * ============
 *
 * In plain English:
 * 
 * 1. We don't promise that this software works.  (But if you find any bugs,
 *    please let us know!)
 * 2. You can use this software for whatever you want.  You don't have to
 *    pay us.
 * 3. You may not pretend that you wrote this software.  If you use it in a
 *    program, you must acknowledge somewhere in your documentation that
 *    you've used the IJG code.
 * 
 * In legalese:
 * 
 * The authors make NO WARRANTY or representation, either express or implied,
 * with respect to this software, its quality, accuracy, merchantability, or
 * fitness for a particular purpose.  This software is provided "AS IS", and
 * you, its user, assume the entire risk as to its quality and accuracy.
 * 
 * This software is copyright (C) 1991, 1992, Thomas G. Lane.
 * All Rights Reserved except as specified below.
 * 
 * Permission is hereby granted to use, copy, modify, and distribute this
 * software (or portions thereof) for any purpose, without fee, subject to
 * these conditions:
 * (1) If any part of the source code for this software is distributed, then
 * this copyright and no-warranty notice must be included unaltered; and any
 * additions, deletions, or changes to the original files must be clearly
 * indicated in accompanying documentation.
 * (2) If only executable code is distributed, then the accompanying
 * documentation must state that "this software is based in part on the
 * work of the Independent JPEG Group".
 * (3) Permission for use of this software is granted only if the user
 * accepts full responsibility for any undesirable consequences; the authors
 * accept NO LIABILITY for damages of any kind.
 * 
 * These conditions apply to any software derived from or based on the IJG
 * code, not just to the unmodified library.  If you use our work, you ought
 * to acknowledge us.
 * 
 * Permission is NOT granted for the use of any IJG author's name or company
 * name in advertising or publicity relating to this software or products
 * derived from it.  This software may be referred to only as
 * "the Independent JPEG Group's software".
 * 
 * We specifically permit and encourage the use of this software as the
 * basis of commercial products, provided that all warranty or liability
 * claims are assumed by the product vendor.
 *
 * 
 * ARCHIVE LOCATIONS
 * =================
 * 
 * The "official" archive site for this software is ftp.uu.net (Internet
 * address 192.48.96.9).  The most recent released version can always be
 * found there in directory graphics/jpeg.  This particular version will
 * be archived as graphics/jpeg/jpegsrc.v6a.tar.gz.  If you are on the
 * Internet, you can retrieve files from ftp.uu.net by standard anonymous
 * FTP.  If you don't have FTP access, UUNET's archives are also available
 * via UUCP; contact help@uunet.uu.net for information on retrieving files
 * that way.
 * 
 * Numerous Internet sites maintain copies of the UUNET files.  However,
 * only ftp.uu.net is guaranteed to have the latest official version.
 * 
 * You can also obtain this software in DOS-compatible "zip" archive
 * format from the SimTel archives (ftp.coast.net:/SimTel/msdos/graphics/),
 * or on CompuServe in the Graphics Support forum (GO CIS:GRAPHSUP),
 * library 12 "JPEG Tools".  Again, these versions may sometimes lag behind
 * the ftp.uu.net release.
 * 
 * The JPEG FAQ (Frequently Asked Questions) article is a useful source of
 * general information about JPEG.  It is updated constantly and therefore
 * is not included in this distribution.  The FAQ is posted every two weeks
 * to Usenet newsgroups comp.graphics.misc, news.answers, and other groups.
 * You can always obtain the latest version from the news.answers archive
 * at rtfm.mit.edu.  By FTP, fetch /pub/usenet/news.answers/jpeg-faq/part1
 * and .../part2.  If you don't have FTP, send e-mail to
 * mail-server@rtfm.mit.edu with body
 *    send usenet/news.answers/jpeg-faq/part1
 *    send usenet/news.answers/jpeg-faq/part2
 * 
 * ==============
 * 
 *
 * This file contains the basic inverse-DCT transformation subroutine.
 *
 * This implementation is based on an algorithm described in
 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
 * The primary algorithm described there uses 11 multiplies and 29 adds.
 * We use their alternate method with 12 multiplies and 32 adds.
 * The advantage of this method is that no data path contains more than one
 * multiplication; this allows a very simple and accurate implementation in
 * scaled fixed-point arithmetic, with a minimal number of shifts.
 * 
 *
 * CHANGES FOR BERKELEY MPEG
 * =========================
 *
 * This file has been altered to use the Berkeley MPEG header files,
 * to add the capability to handle sparse DCT matrices efficiently,
 * and to relabel the inverse DCT function as well as the file
 * (formerly jidctint.c).
 *
 * I've made lots of modifications to attempt to take advantage of the
 * sparse nature of the DCT matrices we're getting.  Although the logic
 * is cumbersome, it's straightforward and the resulting code is much
 * faster.
 *
 * A better way to do this would be to pass in the DCT block as a sparse
 * matrix, perhaps with the difference cases encoded.
 */

#include "jrevdct.h"



  
/* We assume that right shift corresponds to signed division by 2 with
 * rounding towards minus infinity.  This is correct for typical "arithmetic
 * shift" instructions that shift in copies of the sign bit.  But some
 * C compilers implement >> with an unsigned shift.  For these machines you
 * must define RIGHT_SHIFT_IS_UNSIGNED.
 * RIGHT_SHIFT provides a proper signed right shift of an INT32 quantity.
 * It is only applied with constant shift counts.  SHIFT_TEMPS must be
 * included in the variables of any routine using RIGHT_SHIFT.
 */
  
#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define SHIFT_TEMPS     INT32 shift_temp;
#define RIGHT_SHIFT(x,shft)  \
      ((shift_temp = (x)) < 0 ? \
       (shift_temp >> (shft)) | ((~((INT32) 0)) << (32-(shft))) : \
       (shift_temp >> (shft)))
#else
#define SHIFT_TEMPS
#define RIGHT_SHIFT(x,shft)   ((x) >> (shft))
#endif

/*
 * This routine is specialized to the case DCTSIZE = 8.
 */

#if DCTSIZE != 8
  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif


/*
 * A 2-D IDCT can be done by 1-D IDCT on each row followed by 1-D IDCT
 * on each column.  Direct algorithms are also available, but they are
 * much more complex and seem not to be any faster when reduced to code.
 *
 * The poop on this scaling stuff is as follows:
 *
 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
 * larger than the true IDCT outputs.  The final outputs are therefore
 * a factor of N larger than desired; since N=8 this can be cured by
 * a simple right shift at the end of the algorithm.  The advantage of
 * this arrangement is that we save two multiplications per 1-D IDCT,
 * because the y0 and y4 inputs need not be divided by sqrt(N).
 *
 * We have to do addition and subtraction of the integer inputs, which
 * is no problem, and multiplication by fractional constants, which is
 * a problem to do in integer arithmetic.  We multiply all the constants
 * by CONST_SCALE and convert them to integer constants (thus retaining
 * CONST_BITS bits of precision in the constants).  After doing a
 * multiplication we have to divide the product by CONST_SCALE, with proper
 * rounding, to produce the correct output.  This division can be done
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
 * as long as possible so that partial sums can be added together with
 * full fractional precision.
 *
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
 * they are represented to better-than-integral precision.  These outputs
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
 * with the recommended scaling.  (To scale up 12-bit sample data further, an
 * intermediate INT32 array would be needed.)
 *
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
 * shows that the values given below are the most effective.
 */

#ifdef EIGHT_BIT_SAMPLES
#define PASS1_BITS  2
#else
#define PASS1_BITS  1         /* lose a little precision to avoid overflow */
#endif

#define ONE ((INT32) 1)

#define CONST_SCALE (ONE << CONST_BITS)

/* Convert a positive real constant to an integer scaled by CONST_SCALE.
 * IMPORTANT: if your compiler doesn't do this arithmetic at compile time,
 * you will pay a significant penalty in run time.  In that case, figure
 * the correct integer constant values and insert them by hand.
 */

#define FIX(x)    ((INT32) ((x) * CONST_SCALE + 0.5))

/* When adding two opposite-signed fixes, the 0.5 cancels */
#define FIX2(x)   ((INT32) ((x) * CONST_SCALE))

/* Descale and correctly round an INT32 value that's scaled by N bits.
 * We assume RIGHT_SHIFT rounds towards minus infinity, so adding
 * the fudge factor is correct for either sign of X.
 */

#define DESCALE(x,n)  RIGHT_SHIFT((x) + (ONE << ((n)-1)), n)

/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 * For 8-bit samples with the recommended scaling, all the variable
 * and constant values involved are no more than 16 bits wide, so a
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply;
 * this provides a useful speedup on many machines.
 * There is no way to specify a 16x16->32 multiply in portable C, but
 * some C compilers will do the right thing if you provide the correct
 * combination of casts.
 * NB: for 12-bit samples, a full 32-bit multiplication will be needed.
 */

#ifdef EIGHT_BIT_SAMPLES
#ifdef SHORTxSHORT_32         /* may work if 'int' is 32 bits */
#define MULTIPLY(var,const)  (((INT16) (var)) * ((INT16) (const)))
#endif
#ifdef SHORTxLCONST_32        /* known to work with Microsoft C 6.0 */
#define MULTIPLY(var,const)  (((INT16) (var)) * ((INT32) (const)))
#endif
#endif

#ifndef MULTIPLY        /* default definition */
#define MULTIPLY(var,const)  ((var) * (const))
#endif

#ifndef NO_SPARSE_DCT
#define SPARSE_SCALE_FACTOR  8 
#endif

/* Precomputed idct value arrays. */

static DCTELEM PreIDCT[64][64];


/*
 *--------------------------------------------------------------
 *
 * init_pre_idct --
 *
 *  Pre-computes singleton coefficient IDCT values.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */
void init_pre_idct() {
  int i;

  for (i=0; i<64; i++) {
    memset((char *) PreIDCT[i], 0, 64*sizeof(DCTELEM));
    PreIDCT[i][i] = 1 << SPARSE_SCALE_FACTOR;
    j_rev_dct(PreIDCT[i]);
  }

  int pos;
  int rr;
  DCTELEM *ndataptr;

  for(pos=0;pos<64;pos++) {
    ndataptr = PreIDCT[pos];
    
    for(rr=0; rr<4; rr++) {
      for(i=0;i<16;i++) {
      ndataptr[i] = ndataptr[i]/256;
      }
      ndataptr += 16;

    }
  }


    



}

#ifndef NO_SPARSE_DCT
  

/*
 *--------------------------------------------------------------
 *
 * j_rev_dct_sparse --
 *
 *  Performs the inverse DCT on one block of coefficients.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */

void j_rev_dct_sparse (DCTBLOCK data, int pos) {
  short int val;
  register int *dp;
  register int v;
  int quant;

  //  cout << "j_rev_dct_sparse"<<endl;

  /* If DC Coefficient. */
  
  if (pos == 0) {
    dp = (int *)data;
    v = *data;
    quant = 8;

    /* Compute 32 bit value to assign.  This speeds things up a bit */
    if (v < 0) {
        val = -v;
        val += (quant / 2);
        val /= quant;
        val = -val;
    }
    else {
        val = (v + (quant / 2)) / quant;
    }

    v = ((val & 0xffff) | (val << 16));

    dp[0] = v;      dp[1] = v;      dp[2] = v;      dp[3] = v;
    dp[4] = v;      dp[5] = v;      dp[6] = v;      dp[7] = v;
    dp[8] = v;      dp[9] = v;      dp[10] = v;      dp[11] = v;
    dp[12] = v;      dp[13] = v;      dp[14] = v;      dp[15] = v;
    dp[16] = v;      dp[17] = v;      dp[18] = v;      dp[19] = v;
    dp[20] = v;      dp[21] = v;      dp[22] = v;      dp[23] = v;
    dp[24] = v;      dp[25] = v;      dp[26] = v;      dp[27] = v;
    dp[28] = v;      dp[29] = v;      dp[30] = v;      dp[31] = v;

    return;
  }
  //printf("sparse is: %d  val:%8x\n",pos,data[pos]); 

  /*
  j_rev_dct(data);
  return;
  */

  /* Some other coefficient. */

  DCTELEM *dataptr;
  DCTELEM *ndataptr;
  int coeff, rr;



  dataptr = (DCTELEM *)data;
  coeff = dataptr[pos];
  ndataptr = PreIDCT[pos];

  //printf ("COEFFICIENT = %3d, POSITION = %2d\n", coeff, pos);
  coeff=coeff/256;

  for (rr=0; rr<4; rr++) {

    dataptr[0] = (ndataptr[0] * coeff); 
    dataptr[1] = (ndataptr[1] * coeff); 
    dataptr[2] = (ndataptr[2] * coeff); 
    dataptr[3] = (ndataptr[3] * coeff); 
    dataptr[4] = (ndataptr[4] * coeff); 
    dataptr[5] = (ndataptr[5] * coeff); 
    dataptr[6] = (ndataptr[6] * coeff); 
    dataptr[7] = (ndataptr[7] * coeff); 
    dataptr[8] = (ndataptr[8] * coeff); 
    dataptr[9] = (ndataptr[9] * coeff); 
    dataptr[10] = (ndataptr[10] * coeff);
    dataptr[11] = (ndataptr[11] * coeff); 
    dataptr[12] = (ndataptr[12] * coeff); 
    dataptr[13] = (ndataptr[13] * coeff); 
    dataptr[14] = (ndataptr[14] * coeff); 
    dataptr[15] = (ndataptr[15] * coeff); 

    
    dataptr += 16;
    ndataptr += 16;
  }

  dataptr = (DCTELEM *) data;



  return;

}

#else

/*
 *--------------------------------------------------------------
 *
 * j_rev_dct_sparse --
 *
 *  Performs the original inverse DCT on one block of 
 *  coefficients.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */
void j_rev_dct_sparse (DCTBLOCK data,int  pos) {
  j_rev_dct(data);
}
#endif /* SPARSE_DCT */


#ifndef FIVE_DCT

#ifndef ORIG_DCT


/*
 *--------------------------------------------------------------
 *
 * j_rev_dct --
 *
 *  The inverse DCT function.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */
void j_rev_dct (DCTBLOCK data) {


  INT32 tmp0, tmp1, tmp2, tmp3;
  INT32 tmp10, tmp11, tmp12, tmp13;
  INT32 z1, z2, z3, z4, z5;
  INT32 d0, d1, d2, d3, d4, d5, d6, d7;
  register DCTELEM *dataptr;
  int rowctr;
  SHIFT_TEMPS


  /* Pass 1: process rows. */
  /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
  /* furthermore, we scale the results by 2**PASS1_BITS. */

  dataptr = data;

  for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
    /* Due to quantization, we will usually find that many of the input
     * coefficients are zero, especially the AC terms.  We can exploit this
     * by short-circuiting the IDCT calculation for any row in which all
     * the AC terms are zero.  In that case each output is equal to the
     * DC coefficient (with scale factor as needed).
     * With typical images and quantization tables, half or more of the
     * row DCT calculations can be simplified this way.
     */

    register int *idataptr = (int*)dataptr;
    d0 = dataptr[0];
    d1 = dataptr[1];
    if ((d1 == 0) && (idataptr[1] + idataptr[2] + idataptr[3]) == 0) {
      /* AC terms all zero */
      if (d0) {
        /* Compute a 32 bit value to assign. */
        DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS);
        register int v = (dcval & 0xffff) + (dcval << 16);
        
        idataptr[0] = v;
        idataptr[1] = v;
        idataptr[2] = v;
        idataptr[3] = v;
      }
      
      dataptr += DCTSIZE;     /* advance pointer to next row */
      continue;
    }
    d2 = dataptr[2];
    d3 = dataptr[3];
    d4 = dataptr[4];
    d5 = dataptr[5];
    d6 = dataptr[6];
    d7 = dataptr[7];

    /* Even part: reverse the even part of the forward DCT. */
    /* The rotator is sqrt(2)*c(-6). */
    if (d6) {
      if (d4) {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp0 = (d0 + d4) << CONST_BITS;
                tmp1 = (d0 - d4) << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp0 = d4 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp2 - tmp0;
                tmp12 = -(tmp0 + tmp2);
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, - FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp0 = (d0 + d4) << CONST_BITS;
                tmp1 = (d0 - d4) << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;
            } else {
                /* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, - FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp0 = d4 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp2 - tmp0;
                tmp12 = -(tmp0 + tmp2);
            }
          }
      } else {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp0 = d0 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp0 + tmp2;
                tmp12 = tmp0 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp10 = tmp3;
                tmp13 = -tmp3;
                tmp11 = tmp2;
                tmp12 = -tmp2;
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, - FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp0 = d0 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp0 + tmp2;
                tmp12 = tmp0 - tmp2;
            } else {
                /* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, - FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp10 = tmp3;
                tmp13 = -tmp3;
                tmp11 = tmp2;
                tmp12 = -tmp2;
            }
          }
      }
    } else {
      if (d4) {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp0 = (d0 + d4) << CONST_BITS;
                tmp1 = (d0 - d4) << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp0 = d4 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp2 - tmp0;
                tmp12 = -(tmp0 + tmp2);
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
                tmp10 = tmp13 = (d0 + d4) << CONST_BITS;
                tmp11 = tmp12 = (d0 - d4) << CONST_BITS;
            } else {
                /* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
                tmp10 = tmp13 = d4 << CONST_BITS;
                tmp11 = tmp12 = -tmp10;
            }
          }
      } else {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp0 = d0 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp0 + tmp2;
                tmp12 = tmp0 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp10 = tmp3;
                tmp13 = -tmp3;
                tmp11 = tmp2;
                tmp12 = -tmp2;
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
                tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS;
            } else {
                /* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
                tmp10 = tmp13 = tmp11 = tmp12 = 0;
            }
          }
      }
    }


    /* Odd part per figure 8; the matrix is unitary and hence its
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
     */

    if (d7) {
      if (d5) {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
                z1 = d7 + d1;
                z2 = d5 + d3;
                z3 = d7 + d3;
                z4 = d5 + d1;
                z5 = MULTIPLY(z3 + z4, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(z1, - FIX(0.899976223));
                z2 = MULTIPLY(z2, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX(1.961570560));
                z4 = MULTIPLY(z4, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 += z2 + z4;
                tmp2 += z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
                z2 = d5 + d3;
                z3 = d7 + d3;
                z5 = MULTIPLY(z3 + d5, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                z1 = MULTIPLY(d7, - FIX(0.899976223));
                z2 = MULTIPLY(z2, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX(1.961570560));
                z4 = MULTIPLY(d5, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 += z2 + z4;
                tmp2 += z2 + z3;
                tmp3 = z1 + z4;
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
                z1 = d7 + d1;
                z4 = d5 + d1;
                z5 = MULTIPLY(d7 + z4, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(z1, - FIX(0.899976223));
                z2 = MULTIPLY(d5, - FIX(2.562915447));
                z3 = MULTIPLY(d7, - FIX(1.961570560));
                z4 = MULTIPLY(z4, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 += z2 + z4;
                tmp2 = z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
                z5 = MULTIPLY(d7 + d5, FIX(1.175875602));

                tmp0 = MULTIPLY(d7, - FIX2(0.601344887));
                tmp1 = MULTIPLY(d5, - FIX2(0.509795578));
                z1 = MULTIPLY(d7, - FIX(0.899976223));
                z3 = MULTIPLY(d7, - FIX(1.961570560));
                z2 = MULTIPLY(d5, - FIX(2.562915447));
                z4 = MULTIPLY(d5, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z3;
                tmp1 += z4;
                tmp2 = z2 + z3;
                tmp3 = z1 + z4;
            }
          }
      } else {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
                z1 = d7 + d1;
                z3 = d7 + d3;
                z5 = MULTIPLY(z3 + d1, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(z1, - FIX(0.899976223));
                z2 = MULTIPLY(d3, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX(1.961570560));
                z4 = MULTIPLY(d1, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 = z2 + z4;
                tmp2 += z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
                z3 = d7 + d3;
                z5 = MULTIPLY(z3, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, - FIX2(0.601344887));
                tmp2 = MULTIPLY(d3, FIX(0.509795579));
                z1 = MULTIPLY(d7, - FIX(0.899976223));
                z2 = MULTIPLY(d3, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX2(0.785694958));
                
                tmp0 += z3;
                tmp1 = z2 + z5;
                tmp2 += z3;
                tmp3 = z1 + z5;
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
                z1 = d7 + d1;
                z5 = MULTIPLY(z1, FIX(1.175875602));

                tmp0 = MULTIPLY(d7, - FIX2(1.662939224));
                tmp3 = MULTIPLY(d1, FIX2(1.111140466));
                z1 = MULTIPLY(z1, FIX2(0.275899379));
                z3 = MULTIPLY(d7, - FIX(1.961570560));
                z4 = MULTIPLY(d1, - FIX(0.390180644));

                tmp0 += z1;
                tmp1 = z4 + z5;
                tmp2 = z3 + z5;
                tmp3 += z1;
            } else {
                /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
                tmp0 = MULTIPLY(d7, - FIX2(1.387039845));
                tmp1 = MULTIPLY(d7, FIX(1.175875602));
                tmp2 = MULTIPLY(d7, - FIX2(0.785694958));
                tmp3 = MULTIPLY(d7, FIX2(0.275899379));
            }
          }
      }
    } else {
      if (d5) {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
                z2 = d5 + d3;
                z4 = d5 + d1;
                z5 = MULTIPLY(d3 + z4, FIX(1.175875602));
                
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(d1, - FIX(0.899976223));
                z2 = MULTIPLY(z2, - FIX(2.562915447));
                z3 = MULTIPLY(d3, - FIX(1.961570560));
                z4 = MULTIPLY(z4, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 = z1 + z3;
                tmp1 += z2 + z4;
                tmp2 += z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
                z2 = d5 + d3;
                z5 = MULTIPLY(z2, FIX(1.175875602));
                
                tmp1 = MULTIPLY(d5, FIX2(1.662939225));
                tmp2 = MULTIPLY(d3, FIX2(1.111140466));
                z2 = MULTIPLY(z2, - FIX2(1.387039845));
                z3 = MULTIPLY(d3, - FIX(1.961570560));
                z4 = MULTIPLY(d5, - FIX(0.390180644));
                
                tmp0 = z3 + z5;
                tmp1 += z2;
                tmp2 += z2;
                tmp3 = z4 + z5;
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
                z4 = d5 + d1;
                z5 = MULTIPLY(z4, FIX(1.175875602));
                
                tmp1 = MULTIPLY(d5, - FIX2(0.509795578));
                tmp3 = MULTIPLY(d1, FIX2(0.601344887));
                z1 = MULTIPLY(d1, - FIX(0.899976223));
                z2 = MULTIPLY(d5, - FIX(2.562915447));
                z4 = MULTIPLY(z4, FIX2(0.785694958));
                
                tmp0 = z1 + z5;
                tmp2 = z2 + z5;
                tmp1 += z4;
                tmp3 += z4;
            } else {
                /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
                tmp0 = MULTIPLY(d5, FIX(1.175875602));
                tmp1 = MULTIPLY(d5, FIX2(0.275899380));
                tmp2 = MULTIPLY(d5, - FIX2(1.387039845));
                tmp3 = MULTIPLY(d5, FIX2(0.785694958));
            }
          }
      } else {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
                z5 = d3 + d1;

                tmp2 = MULTIPLY(d3, - FIX(1.451774981));
                tmp3 = MULTIPLY(d1, (FIX(0.211164243) - 1));
                z1 = MULTIPLY(d1, FIX(1.061594337));
                z2 = MULTIPLY(d3, - FIX(2.172734803));
                z4 = MULTIPLY(z5, FIX(0.785694958));
                z5 = MULTIPLY(z5, FIX(1.175875602));
                
                tmp0 = z1 - z4;
                tmp1 = z2 + z4;
                tmp2 += z5;
                tmp3 += z5;
            } else {
                /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
                tmp0 = MULTIPLY(d3, - FIX2(0.785694958));
                tmp1 = MULTIPLY(d3, - FIX2(1.387039845));
                tmp2 = MULTIPLY(d3, - FIX2(0.275899379));
                tmp3 = MULTIPLY(d3, FIX(1.175875602));
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
                tmp0 = MULTIPLY(d1, FIX2(0.275899379));
                tmp1 = MULTIPLY(d1, FIX2(0.785694958));
                tmp2 = MULTIPLY(d1, FIX(1.175875602));
                tmp3 = MULTIPLY(d1, FIX2(1.387039845));
            } else {
                /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
                tmp0 = tmp1 = tmp2 = tmp3 = 0;
            }
          }
      }
    }

    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

    dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
    dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
    dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
    dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
    dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
    dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
    dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
    dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);

    dataptr += DCTSIZE;       /* advance pointer to next row */
  }

  /* Pass 2: process columns. */
  /* Note that we must descale the results by a factor of 8 == 2**3, */
  /* and also undo the PASS1_BITS scaling. */

  dataptr = data;
  for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
    /* Columns of zeroes can be exploited in the same way as we did with rows.
     * However, the row calculation has created many nonzero AC terms, so the
     * simplification applies less often (typically 5% to 10% of the time).
     * On machines with very fast multiplication, it's possible that the
     * test takes more time than it's worth.  In that case this section
     * may be commented out.
     */

    d0 = dataptr[DCTSIZE*0];
    d1 = dataptr[DCTSIZE*1];
    d2 = dataptr[DCTSIZE*2];
    d3 = dataptr[DCTSIZE*3];
    d4 = dataptr[DCTSIZE*4];
    d5 = dataptr[DCTSIZE*5];
    d6 = dataptr[DCTSIZE*6];
    d7 = dataptr[DCTSIZE*7];

    /* Even part: reverse the even part of the forward DCT. */
    /* The rotator is sqrt(2)*c(-6). */
    if (d6) {
      if (d4) {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp0 = (d0 + d4) << CONST_BITS;
                tmp1 = (d0 - d4) << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp0 = d4 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp2 - tmp0;
                tmp12 = -(tmp0 + tmp2);
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, - FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp0 = (d0 + d4) << CONST_BITS;
                tmp1 = (d0 - d4) << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;
            } else {
                /* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, -FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp0 = d4 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp2 - tmp0;
                tmp12 = -(tmp0 + tmp2);
            }
          }
      } else {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp0 = d0 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp0 + tmp2;
                tmp12 = tmp0 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
                z1 = MULTIPLY(d2 + d6, FIX(0.541196100));
                tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065));
                tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865));

                tmp10 = tmp3;
                tmp13 = -tmp3;
                tmp11 = tmp2;
                tmp12 = -tmp2;
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, - FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp0 = d0 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp0 + tmp2;
                tmp12 = tmp0 - tmp2;
            } else {
                /* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
                tmp2 = MULTIPLY(d6, - FIX2(1.306562965));
                tmp3 = MULTIPLY(d6, FIX(0.541196100));

                tmp10 = tmp3;
                tmp13 = -tmp3;
                tmp11 = tmp2;
                tmp12 = -tmp2;
            }
          }
      }
    } else {
      if (d4) {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp0 = (d0 + d4) << CONST_BITS;
                tmp1 = (d0 - d4) << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp1 + tmp2;
                tmp12 = tmp1 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp0 = d4 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp2 - tmp0;
                tmp12 = -(tmp0 + tmp2);
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
                tmp10 = tmp13 = (d0 + d4) << CONST_BITS;
                tmp11 = tmp12 = (d0 - d4) << CONST_BITS;
            } else {
                /* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
                tmp10 = tmp13 = d4 << CONST_BITS;
                tmp11 = tmp12 = -tmp10;
            }
          }
      } else {
          if (d2) {
            if (d0) {
                /* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp0 = d0 << CONST_BITS;

                tmp10 = tmp0 + tmp3;
                tmp13 = tmp0 - tmp3;
                tmp11 = tmp0 + tmp2;
                tmp12 = tmp0 - tmp2;
            } else {
                /* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
                tmp2 = MULTIPLY(d2, FIX(0.541196100));
                tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5)));

                tmp10 = tmp3;
                tmp13 = -tmp3;
                tmp11 = tmp2;
                tmp12 = -tmp2;
            }
          } else {
            if (d0) {
                /* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
                tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS;
            } else {
                /* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
                tmp10 = tmp13 = tmp11 = tmp12 = 0;
            }
          }
      }
    }

    /* Odd part per figure 8; the matrix is unitary and hence its
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
     */
    if (d7) {
      if (d5) {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
                z1 = d7 + d1;
                z2 = d5 + d3;
                z3 = d7 + d3;
                z4 = d5 + d1;
                z5 = MULTIPLY(z3 + z4, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(z1, - FIX(0.899976223));
                z2 = MULTIPLY(z2, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX(1.961570560));
                z4 = MULTIPLY(z4, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 += z2 + z4;
                tmp2 += z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
                z2 = d5 + d3;
                z3 = d7 + d3;
                z5 = MULTIPLY(z3 + d5, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                z1 = MULTIPLY(d7, - FIX(0.899976223));
                z2 = MULTIPLY(z2, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX(1.961570560));
                z4 = MULTIPLY(d5, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 += z2 + z4;
                tmp2 += z2 + z3;
                tmp3 = z1 + z4;
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
                z1 = d7 + d1;
                z4 = d5 + d1;
                z5 = MULTIPLY(d7 + z4, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(z1, - FIX(0.899976223));
                z2 = MULTIPLY(d5, - FIX(2.562915447));
                z3 = MULTIPLY(d7, - FIX(1.961570560));
                z4 = MULTIPLY(z4, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 += z2 + z4;
                tmp2 = z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
                z5 = MULTIPLY(d5 + d7, FIX(1.175875602));

                tmp0 = MULTIPLY(d7, - FIX2(0.601344887)); 
                tmp1 = MULTIPLY(d5, - FIX2(0.509795578));
                z1 = MULTIPLY(d7, - FIX(0.899976223));
                z3 = MULTIPLY(d7, - FIX(1.961570560));
                z2 = MULTIPLY(d5, - FIX(2.562915447));
                z4 = MULTIPLY(d5, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z3;
                tmp1 += z4;
                tmp2 = z2 + z3;
                tmp3 = z1 + z4;
            }
          }
      } else {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
                z1 = d7 + d1;
                z3 = d7 + d3;
                z5 = MULTIPLY(z3 + d1, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, FIX(0.298631336)); 
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(z1, - FIX(0.899976223));
                z2 = MULTIPLY(d3, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX(1.961570560));
                z4 = MULTIPLY(d1, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 += z1 + z3;
                tmp1 = z2 + z4;
                tmp2 += z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
                z3 = d7 + d3;
                z5 = MULTIPLY(z3, FIX(1.175875602));
                
                tmp0 = MULTIPLY(d7, - FIX2(0.601344887)); 
                z1 = MULTIPLY(d7, - FIX(0.899976223));
                tmp2 = MULTIPLY(d3, FIX(0.509795579));
                z2 = MULTIPLY(d3, - FIX(2.562915447));
                z3 = MULTIPLY(z3, - FIX2(0.785694958));
                
                tmp0 += z3;
                tmp1 = z2 + z5;
                tmp2 += z3;
                tmp3 = z1 + z5;
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
                z1 = d7 + d1;
                z5 = MULTIPLY(z1, FIX(1.175875602));

                tmp0 = MULTIPLY(d7, - FIX2(1.662939224)); 
                tmp3 = MULTIPLY(d1, FIX2(1.111140466));
                z1 = MULTIPLY(z1, FIX2(0.275899379));
                z3 = MULTIPLY(d7, - FIX(1.961570560));
                z4 = MULTIPLY(d1, - FIX(0.390180644));

                tmp0 += z1;
                tmp1 = z4 + z5;
                tmp2 = z3 + z5;
                tmp3 += z1;
            } else {
                /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
                tmp0 = MULTIPLY(d7, - FIX2(1.387039845));
                tmp1 = MULTIPLY(d7, FIX(1.175875602));
                tmp2 = MULTIPLY(d7, - FIX2(0.785694958));
                tmp3 = MULTIPLY(d7, FIX2(0.275899379));
            }
          }
      }
    } else {
      if (d5) {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
                z2 = d5 + d3;
                z4 = d5 + d1;
                z5 = MULTIPLY(d3 + z4, FIX(1.175875602));
                
                tmp1 = MULTIPLY(d5, FIX(2.053119869));
                tmp2 = MULTIPLY(d3, FIX(3.072711026));
                tmp3 = MULTIPLY(d1, FIX(1.501321110));
                z1 = MULTIPLY(d1, - FIX(0.899976223));
                z2 = MULTIPLY(z2, - FIX(2.562915447));
                z3 = MULTIPLY(d3, - FIX(1.961570560));
                z4 = MULTIPLY(z4, - FIX(0.390180644));
                
                z3 += z5;
                z4 += z5;
                
                tmp0 = z1 + z3;
                tmp1 += z2 + z4;
                tmp2 += z2 + z3;
                tmp3 += z1 + z4;
            } else {
                /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
                z2 = d5 + d3;
                z5 = MULTIPLY(z2, FIX(1.175875602));

                tmp1 = MULTIPLY(d5, FIX2(1.662939225));
                tmp2 = MULTIPLY(d3, FIX2(1.111140466));
                z2 = MULTIPLY(z2, - FIX2(1.387039845));
                z3 = MULTIPLY(d3, - FIX(1.961570560));
                z4 = MULTIPLY(d5, - FIX(0.390180644));
                
                tmp0 = z3 + z5;
                tmp1 += z2;
                tmp2 += z2;
                tmp3 = z4 + z5;
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
                z4 = d5 + d1;
                z5 = MULTIPLY(z4, FIX(1.175875602));
                
                tmp1 = MULTIPLY(d5, - FIX2(0.509795578));
                tmp3 = MULTIPLY(d1, FIX2(0.601344887));
                z1 = MULTIPLY(d1, - FIX(0.899976223));
                z2 = MULTIPLY(d5, - FIX(2.562915447));
                z4 = MULTIPLY(z4, FIX2(0.785694958));
                
                tmp0 = z1 + z5;
                tmp1 += z4;
                tmp2 = z2 + z5;
                tmp3 += z4;
            } else {
                /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
                tmp0 = MULTIPLY(d5, FIX(1.175875602));
                tmp1 = MULTIPLY(d5, FIX2(0.275899380));
                tmp2 = MULTIPLY(d5, - FIX2(1.387039845));
                tmp3 = MULTIPLY(d5, FIX2(0.785694958));
            }
          }
      } else {
          if (d3) {
            if (d1) {
                /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
                z5 = d3 + d1;

                tmp2 = MULTIPLY(d3, - FIX(1.451774981));
                tmp3 = MULTIPLY(d1, (FIX(0.211164243) - 1));
                z1 = MULTIPLY(d1, FIX(1.061594337));
                z2 = MULTIPLY(d3, - FIX(2.172734803));
                z4 = MULTIPLY(z5, FIX(0.785694958));
                z5 = MULTIPLY(z5, FIX(1.175875602));
                
                tmp0 = z1 - z4;
                tmp1 = z2 + z4;
                tmp2 += z5;
                tmp3 += z5;
            } else {
                /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
                tmp0 = MULTIPLY(d3, - FIX2(0.785694958));
                tmp1 = MULTIPLY(d3, - FIX2(1.387039845));
                tmp2 = MULTIPLY(d3, - FIX2(0.275899379));
                tmp3 = MULTIPLY(d3, FIX(1.175875602));
            }
          } else {
            if (d1) {
                /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
                tmp0 = MULTIPLY(d1, FIX2(0.275899379));
                tmp1 = MULTIPLY(d1, FIX2(0.785694958));
                tmp2 = MULTIPLY(d1, FIX(1.175875602));
                tmp3 = MULTIPLY(d1, FIX2(1.387039845));
            } else {
                /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
                tmp0 = tmp1 = tmp2 = tmp3 = 0;
            }
          }
      }
    }

    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0,
                                 CONST_BITS+PASS1_BITS+3);
    
    dataptr++;                /* advance pointer to next column */
  }
}

#else



/*
 *--------------------------------------------------------------
 *
 * j_rev_dct --
 *
 *  The original inverse DCT function.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */
void j_rev_dct (DCTBLOCK data)
{
  INT32 tmp0, tmp1, tmp2, tmp3;
  INT32 tmp10, tmp11, tmp12, tmp13;
  INT32 z1, z2, z3, z4, z5;
  register DCTELEM *dataptr;
  int rowctr;
  SHIFT_TEMPS

  /* Pass 1: process rows. */
  /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
  /* furthermore, we scale the results by 2**PASS1_BITS. */

  dataptr = data;
  for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
    /* Due to quantization, we will usually find that many of the input
     * coefficients are zero, especially the AC terms.  We can exploit this
     * by short-circuiting the IDCT calculation for any row in which all
     * the AC terms are zero.  In that case each output is equal to the
     * DC coefficient (with scale factor as needed).
     * With typical images and quantization tables, half or more of the
     * row DCT calculations can be simplified this way.
     */

    if ((dataptr[1] | dataptr[2] | dataptr[3] | dataptr[4] |
       dataptr[5] | dataptr[6] | dataptr[7]) == 0) {
      /* AC terms all zero */
      DCTELEM dcval = (DCTELEM) (dataptr[0] << PASS1_BITS);
      
      dataptr[0] = dcval;
      dataptr[1] = dcval;
      dataptr[2] = dcval;
      dataptr[3] = dcval;
      dataptr[4] = dcval;
      dataptr[5] = dcval;
      dataptr[6] = dcval;
      dataptr[7] = dcval;
      
      dataptr += DCTSIZE;     /* advance pointer to next row */
      continue;
    }

    /* Even part: reverse the even part of the forward DCT. */
    /* The rotator is sqrt(2)*c(-6). */

    z2 = (INT32) dataptr[2];
    z3 = (INT32) dataptr[6];

    z1 = MULTIPLY(z2 + z3, FIX(0.541196100));
    tmp2 = z1 + MULTIPLY(z3, - FIX(1.847759065));
    tmp3 = z1 + MULTIPLY(z2, FIX(0.765366865));

    tmp0 = ((INT32) dataptr[0] + (INT32) dataptr[4]) << CONST_BITS;
    tmp1 = ((INT32) dataptr[0] - (INT32) dataptr[4]) << CONST_BITS;

    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;
    
    /* Odd part per figure 8; the matrix is unitary and hence its
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
     */

    tmp0 = (INT32) dataptr[7];
    tmp1 = (INT32) dataptr[5];
    tmp2 = (INT32) dataptr[3];
    tmp3 = (INT32) dataptr[1];

    z1 = tmp0 + tmp3;
    z2 = tmp1 + tmp2;
    z3 = tmp0 + tmp2;
    z4 = tmp1 + tmp3;
    z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); /* sqrt(2) * c3 */
    
    tmp0 = MULTIPLY(tmp0, FIX(0.298631336)); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp1 = MULTIPLY(tmp1, FIX(2.053119869)); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp2 = MULTIPLY(tmp2, FIX(3.072711026)); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp3 = MULTIPLY(tmp3, FIX(1.501321110)); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, - FIX(0.899976223)); /* sqrt(2) * (c7-c3) */
    z2 = MULTIPLY(z2, - FIX(2.562915447)); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, - FIX(1.961570560)); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, - FIX(0.390180644)); /* sqrt(2) * (c5-c3) */
    
    z3 += z5;
    z4 += z5;
    
    tmp0 += z1 + z3;
    tmp1 += z2 + z4;
    tmp2 += z2 + z3;
    tmp3 += z1 + z4;

    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

    dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
    dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
    dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
    dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
    dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
    dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
    dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
    dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);

    dataptr += DCTSIZE;       /* advance pointer to next row */
  }

  /* Pass 2: process columns. */
  /* Note that we must descale the results by a factor of 8 == 2**3, */
  /* and also undo the PASS1_BITS scaling. */

  dataptr = data;
  for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
    /* Columns of zeroes can be exploited in the same way as we did with rows.
     * However, the row calculation has created many nonzero AC terms, so the
     * simplification applies less often (typically 5% to 10% of the time).
     * On machines with very fast multiplication, it's possible that the
     * test takes more time than it's worth.  In that case this section
     * may be commented out.
     */

#ifndef NO_ZERO_COLUMN_TEST
    if ((dataptr[DCTSIZE*1] | dataptr[DCTSIZE*2] | dataptr[DCTSIZE*3] |
       dataptr[DCTSIZE*4] | dataptr[DCTSIZE*5] | dataptr[DCTSIZE*6] |
       dataptr[DCTSIZE*7]) == 0) {
      /* AC terms all zero */
      DCTELEM dcval = (DCTELEM) DESCALE((INT32) dataptr[0], PASS1_BITS+3);
      
      dataptr[DCTSIZE*0] = dcval;
      dataptr[DCTSIZE*1] = dcval;
      dataptr[DCTSIZE*2] = dcval;
      dataptr[DCTSIZE*3] = dcval;
      dataptr[DCTSIZE*4] = dcval;
      dataptr[DCTSIZE*5] = dcval;
      dataptr[DCTSIZE*6] = dcval;
      dataptr[DCTSIZE*7] = dcval;
      
      dataptr++;        /* advance pointer to next column */
      continue;
    }
#endif

    /* Even part: reverse the even part of the forward DCT. */
    /* The rotator is sqrt(2)*c(-6). */

    z2 = (INT32) dataptr[DCTSIZE*2];
    z3 = (INT32) dataptr[DCTSIZE*6];

    z1 = MULTIPLY(z2 + z3, FIX(0.541196100));
    tmp2 = z1 + MULTIPLY(z3, - FIX(1.847759065));
    tmp3 = z1 + MULTIPLY(z2, FIX(0.765366865));

    tmp0 = ((INT32) dataptr[DCTSIZE*0] + (INT32) dataptr[DCTSIZE*4]) << CONST_BITS;
    tmp1 = ((INT32) dataptr[DCTSIZE*0] - (INT32) dataptr[DCTSIZE*4]) << CONST_BITS;

    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;
    
    /* Odd part per figure 8; the matrix is unitary and hence its
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
     */

    tmp0 = (INT32) dataptr[DCTSIZE*7];
    tmp1 = (INT32) dataptr[DCTSIZE*5];
    tmp2 = (INT32) dataptr[DCTSIZE*3];
    tmp3 = (INT32) dataptr[DCTSIZE*1];

    z1 = tmp0 + tmp3;
    z2 = tmp1 + tmp2;
    z3 = tmp0 + tmp2;
    z4 = tmp1 + tmp3;
    z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); /* sqrt(2) * c3 */
    
    tmp0 = MULTIPLY(tmp0, FIX(0.298631336)); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp1 = MULTIPLY(tmp1, FIX(2.053119869)); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp2 = MULTIPLY(tmp2, FIX(3.072711026)); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp3 = MULTIPLY(tmp3, FIX(1.501321110)); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, - FIX(0.899976223)); /* sqrt(2) * (c7-c3) */
    z2 = MULTIPLY(z2, - FIX(2.562915447)); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, - FIX(1.961570560)); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, - FIX(0.390180644)); /* sqrt(2) * (c5-c3) */
    
    z3 += z5;
    z4 += z5;
    
    tmp0 += z1 + z3;
    tmp1 += z2 + z4;
    tmp2 += z2 + z3;
    tmp3 += z1 + z4;

    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0,
                                 CONST_BITS+PASS1_BITS+3);
    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0,
                                 CONST_BITS+PASS1_BITS+3);
    
    dataptr++;                /* advance pointer to next column */
  }
}


#endif /* ORIG_DCT */
#endif /* FIVE_DCT */


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