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/*

 * 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 <string.h>

#include "video.h"

#include "proto.h"

#define GLOBAL                  /* a function referenced thru EXTERNs */

/* 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]);

  }

}

#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 (data, pos)

     DCTBLOCK data;

     int pos;

{

  short int val;

  register int *dp;

  register int v;

  int quant;

#ifdef SPARSE_AC

  register DCTELEM *dataptr;

  DCTELEM *ndataptr;

  int coeff, rr;

  DCTBLOCK tmpdata, tmp2data;

  DCTELEM *tmpdataptr, *tmp2dataptr;

  int printFlag = 1;

#endif

  /* 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 >> 1);

        val /= quant;

        val = -val;

    }

    else {

        val = (v + (quant >> 1)) / 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;

  }

  /* Some other coefficient. */

#ifdef SPARSE_AC

  dataptr = (DCTELEM *)data;

  coeff = dataptr[pos];

  ndataptr = PreIDCT[pos];

  printf ("\n");

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

  for (v=0; v<64; v++) {

    memcpy((char *) tmpdata, data, 64*sizeof(DCTELEM));

  }

  tmpdataptr = (DCTELEM *)tmpdata;

  for (v=0; v<64; v++) {

    memcpy((char *) tmp2data, data, 64*sizeof(DCTELEM));

  }

  tmp2dataptr = (DCTELEM *)tmp2data;

#ifdef DEBUG

  printf ("original DCTBLOCK:\n");

  for (rr=0; rr<8; rr++) {

    for (v=0; v<8; v++) {

          if (dataptr[8*rr+v] != tmpdataptr[8*rr+v])

                fprintf(stderr, "Error in copy\n");

          printf ("%3d ", dataptr[8*rr+v]);

    }

    printf("\n");

  }

#endif

  printf("\n");

  for (rr=0; rr<4; rr++) {

    dataptr[0] = (ndataptr[0] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[1] = (ndataptr[1] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[2] = (ndataptr[2] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[3] = (ndataptr[3] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[4] = (ndataptr[4] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[5] = (ndataptr[5] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[6] = (ndataptr[6] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[7] = (ndataptr[7] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[8] = (ndataptr[8] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[9] = (ndataptr[9] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[10] = (ndataptr[10] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[11] = (ndataptr[11] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[12] = (ndataptr[12] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[13] = (ndataptr[13] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[14] = (ndataptr[14] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr[15] = (ndataptr[15] * coeff) >> SPARSE_SCALE_FACTOR;

    dataptr += 16;

    ndataptr += 16;

  }

  dataptr = (DCTELEM *) data;

#ifdef DEBUG 

  printf ("sparse IDCT:\n");

  for (rr=0; rr<8; rr++) {

    for (v=0; v<8; v++) {

          printf ("%3d ", dataptr[8*rr+v]);

    }

    printf("\n");

  }

  printf("\n");

#endif /* DEBUG */

#else  /* NO_SPARSE_AC */

#ifdef FLOATDCT

  if (qualityFlag)

        float_idct(data);

  else

#endif /* FLOATDCT */

        j_rev_dct(data);

#endif /* SPARSE_AC */

  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 (data, pos)

     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 (data)

     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 = 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 = 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 = 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 = 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;