/*
 * jrevdct.c
 *
 * Copyright (C) 1991, 1992, Thomas G. Lane.
 * This file is part of the Independent JPEG Group's software.
 * For conditions of distribution and use, see the accompanying README file.
 *
 * 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.
 * 
 * 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.
 */

/************************************************************************
                            R C S Information
*************************************************************************/

/* $Log: jrevdct.c,v $
 * Revision 1.4  1994/01/12  19:35:24  daf
 * Added RCS info.
 *
 * revision 1.3    locked by: daf;
 * date: 1994/01/11 20:59:46;  author: daf;  state: Exp;  lines: +2 -0
 * *** empty log message ***
 * 
 * revision 1.2
 * date: 1994/01/11 20:54:43;  author: daf;  state: Exp;  lines: +2 -0
 * Modified for PC compatibility
 * 
 * revision 1.1
 * date: 1994/01/07 17:05:21;  author: daf;  state: Exp;
 * Initial revision
*/

#ifndef __WATCOMC__
#include <memory.h>
#else
#include <string.h>
#endif
#include "all.h"
#include "ansi.h"
#include "dct.h"


#define CONST_BITS 13


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

#define FIX_0_211164243	(2048-256)		/* 1792 ~ 1730 */
#define FIX_0_275899380	(2048+256)		/* 2304 ~ 2260 */
#define FIX_0_298631336	(2048+512)		/* 2560 ~ 2446 */
#define FIX_0_390180644	(2048+1024+128)		/* 3200 ~ 3196 */
#define FIX_0_509795579	(4096+64)		/* 4160 ~ 4176 */
#define FIX_0_541196100	(4096+512)		/* 4608 ~ 4433 */
#define FIX_0_601344887	(4096+1024)		/* 5120 ~ 4926 */
#define FIX_0_765366865	(4096+2048)		/* 6144 ~ 6270 */
#define FIX_0_785694958	(4096+2048+512)		/* 6656 ~ 6436 */
#define FIX_0_899976223	(8192-1024)		/* 7168 ~ 7373 */
#define FIX_1_061594337	(8192+512)		/* 8704 ~ 8697 */
#define FIX_1_111140466	(8192+1024)		/* 9216 ~ 9102 */
#define FIX_1_175875602	(8192+2048-512)		/* 9728 ~ 9633 */
#define FIX_1_306562965	(8192+2048+512)		/* 10752 ~ 10703 */
#define FIX_1_387039845	(8192+4096-1024)	/* 11264 ~ 11363 */
#define FIX_1_451774981	(8192+4096-512)		/* 11776 ~ 11893 */
#define FIX_1_501321110	(8192+4096)		/* 12288 ~ 12299 */
#define FIX_1_662939225	(8192+4096+1024)	/* 13312 ~ 13623 */
#define FIX_1_847759065	(16384-1024)		/* 15360 ~ 15137 */
#define FIX_1_961570560	(16384-256)		/* 16128 ~ 16069 */
#define FIX_2_053119869	(16384+512)		/* 16896 ~ 16819 */
#define FIX_2_172734803	(16384+1024)		/* 17408 ~ 17799 */
#define FIX_2_562915447	(16384+4096+512)	/* 20992 ~ 20995 */
#define FIX_3_072711026	(16384+8192+512)	/* 25088 ~ 25172 */

/* 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), 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


/* Precomputed idct value arrays. */

static DCTELEM PreIDCT[64][64];



/* Pre compute singleton coefficient IDCT values. */
void
init_pre_idct()
{
  int i;

  void j_rev_dct();
  
  for (i=0; i<64; i++) {
    memset((char *) PreIDCT[i], 0, 64*sizeof(DCTELEM));
    PreIDCT[i][i] = 2048;
    j_rev_dct(PreIDCT[i]);
  }
}

#ifndef ORIG_DCT
  

/*
 * Perform the inverse DCT on one block of coefficients.
 */

void
j_rev_dct_sparse(data, pos)
    DCTBLOCK data;
    int pos;
{
  register DCTELEM *dataptr;
  short int val;
  DCTELEM *ndataptr;
  int coeff, rr;
  register int *dp;
  register int v;

  /* If DC Coefficient. */
  
  if (pos == 0) {
    dp = (int *)data;
    v = *data;
    /* Compute 32 bit value to assign.  This speeds things up a bit */
    if (v < 0) val = (v-3)>>3;
    else val = (v+4)>>3;
    v = val | (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. */
  dataptr = (DCTELEM *)data;
  coeff = dataptr[pos];
  ndataptr = PreIDCT[pos];

  for (rr=0; rr<4; rr++) {
    dataptr[0] = (ndataptr[0] * coeff) >> (CONST_BITS-2);
    dataptr[1] = (ndataptr[1] * coeff) >> (CONST_BITS-2);
    dataptr[2] = (ndataptr[2] * coeff) >> (CONST_BITS-2);
    dataptr[3] = (ndataptr[3] * coeff) >> (CONST_BITS-2);
    dataptr[4] = (ndataptr[4] * coeff) >> (CONST_BITS-2);
    dataptr[5] = (ndataptr[5] * coeff) >> (CONST_BITS-2);
    dataptr[6] = (ndataptr[6] * coeff) >> (CONST_BITS-2);
    dataptr[7] = (ndataptr[7] * coeff) >> (CONST_BITS-2);
    dataptr[8] = (ndataptr[8] * coeff) >> (CONST_BITS-2);
    dataptr[9] = (ndataptr[9] * coeff) >> (CONST_BITS-2);
    dataptr[10] = (ndataptr[10] * coeff) >> (CONST_BITS-2);
    dataptr[11] = (ndataptr[11] * coeff) >> (CONST_BITS-2);
    dataptr[12] = (ndataptr[12] * coeff) >> (CONST_BITS-2);
    dataptr[13] = (ndataptr[13] * coeff) >> (CONST_BITS-2);
    dataptr[14] = (ndataptr[14] * coeff) >> (CONST_BITS-2);
    dataptr[15] = (ndataptr[15] * coeff) >> (CONST_BITS-2);
    dataptr += 16;
    ndataptr += 16;
  }
  return;
}


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) & 0xffff0000);
	  
	  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, FIX_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, FIX_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, FIX_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, FIX_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);

		    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);

		    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);

		    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);

		    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 */
		    tmp0 = MULTIPLY(-d7, FIX_0_601344887); 
		    z1 = MULTIPLY(-d7, FIX_0_899976223);
		    z3 = MULTIPLY(-d7, FIX_1_961570560);
		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
		    z2 = MULTIPLY(-d5, FIX_2_562915447);
		    z4 = MULTIPLY(-d5, FIX_0_390180644);
		    z5 = MULTIPLY(d5 + d7, FIX_1_175875602);
		    
		    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;
		    
		    tmp0 = MULTIPLY(-d7, FIX_0_601344887); 
		    z1 = MULTIPLY(-d7, FIX_0_899976223);
		    tmp2 = MULTIPLY(d3, FIX_0_509795579);
		    z2 = MULTIPLY(-d3, FIX_2_562915447);
		    z5 = MULTIPLY(z3, FIX_1_175875602);
		    z3 = MULTIPLY(-z3, FIX_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);

		    z1 = MULTIPLY(z1, FIX_0_275899380);
		    z3 = MULTIPLY(-d7, FIX_1_961570560);
		    tmp0 = MULTIPLY(-d7, FIX_1_662939225); 
		    z4 = MULTIPLY(-d1, FIX_0_390180644);
		    tmp3 = MULTIPLY(d1, FIX_1_111140466);

		    tmp0 += z1;
		    tmp1 = z4 + z5;
		    tmp2 = z3 + z5;
		    tmp3 += z1;
		} else {
		    /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
		    tmp0 = MULTIPLY(-d7, FIX_1_387039845);
		    tmp1 = MULTIPLY(d7, FIX_1_175875602);
		    tmp2 = MULTIPLY(-d7, FIX_0_785694958);
		    tmp3 = MULTIPLY(d7, FIX_0_275899380);
		}
	    }
	}
    } 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, FIX_1_662939225);
		    z4 = MULTIPLY(-d5, FIX_0_390180644);
		    z2 = MULTIPLY(-z2, FIX_1_387039845);
		    tmp2 = MULTIPLY(d3, FIX_1_111140466);
		    z3 = MULTIPLY(-d3, FIX_1_961570560);
		    
		    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);
		    z1 = MULTIPLY(-d1, FIX_0_899976223);
		    tmp3 = MULTIPLY(d1, FIX_0_601344887);
		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
		    z2 = MULTIPLY(-d5, FIX_2_562915447);
		    z4 = MULTIPLY(z4, FIX_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, FIX_0_275899380);
		    tmp2 = MULTIPLY(-d5, FIX_1_387039845);
		    tmp3 = MULTIPLY(d5, FIX_0_785694958);
		}
	    }
	} else {
	    if (d3) {
		if (d1) {
		    /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
		    z5 = d1 + d3;
		    tmp3 = MULTIPLY(d1, FIX_0_211164243);
		    tmp2 = MULTIPLY(-d3, FIX_1_451774981);
		    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, FIX_0_785694958);
		    tmp1 = MULTIPLY(-d3, FIX_1_387039845);
		    tmp2 = MULTIPLY(-d3, FIX_0_275899380);
		    tmp3 = MULTIPLY(d3, FIX_1_175875602);
		}
	    } else {
		if (d1) {
		    /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
		    tmp0 = MULTIPLY(d1, FIX_0_275899380);
		    tmp1 = MULTIPLY(d1, FIX_0_785694958);
		    tmp2 = MULTIPLY(d1, FIX_1_175875602);
		    tmp3 = MULTIPLY(d1, FIX_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, FIX_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, FIX_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, FIX_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, FIX_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);

		    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);

		    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);

		    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);

		    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 */
		    z1 = d7;
		    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;
		    z2 = d5;
		    z3 = d7;
		    z4 = d5 + d1;
		    z5 = MULTIPLY(z3 + 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 */
		    tmp0 = MULTIPLY(-d7, FIX_0_601344887); 
		    z1 = MULTIPLY(-d7, FIX_0_899976223);
		    z3 = MULTIPLY(-d7, FIX_1_961570560);
		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
		    z2 = MULTIPLY(-d5, FIX_2_562915447);
		    z4 = MULTIPLY(-d5, FIX_0_390180644);
		    z5 = MULTIPLY(d5 + d7, FIX_1_175875602);
		    
		    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;
		    
		    tmp0 = MULTIPLY(-d7, FIX_0_601344887); 
		    z1 = MULTIPLY(-d7, FIX_0_899976223);
		    tmp2 = MULTIPLY(d3, FIX_0_509795579);
		    z2 = MULTIPLY(-d3, FIX_2_562915447);
		    z5 = MULTIPLY(z3, FIX_1_175875602);
		    z3 = MULTIPLY(-z3, FIX_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);

		    z1 = MULTIPLY(z1, FIX_0_275899380);
		    z3 = MULTIPLY(-d7, FIX_1_961570560);
		    tmp0 = MULTIPLY(-d7, FIX_1_662939225); 
		    z4 = MULTIPLY(-d1, FIX_0_390180644);
		    tmp3 = MULTIPLY(d1, FIX_1_111140466);

		    tmp0 += z1;
		    tmp1 = z4 + z5;
		    tmp2 = z3 + z5;
		    tmp3 += z1;
		} else {
		    /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
		    tmp0 = MULTIPLY(-d7, FIX_1_387039845);
		    tmp1 = MULTIPLY(d7, FIX_1_175875602);
		    tmp2 = MULTIPLY(-d7, FIX_0_785694958);
		    tmp3 = MULTIPLY(d7, FIX_0_275899380);
		}
	    }
	}
    } 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, FIX_1_662939225);
		    z4 = MULTIPLY(-d5, FIX_0_390180644);
		    z2 = MULTIPLY(-z2, FIX_1_387039845);
		    tmp2 = MULTIPLY(d3, FIX_1_111140466);
		    z3 = MULTIPLY(-d3, FIX_1_961570560);
		    
		    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);
		    z1 = MULTIPLY(-d1, FIX_0_899976223);
		    tmp3 = MULTIPLY(d1, FIX_0_601344887);
		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
		    z2 = MULTIPLY(-d5, FIX_2_562915447);
		    z4 = MULTIPLY(z4, FIX_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, FIX_0_275899380);
		    tmp2 = MULTIPLY(-d5, FIX_1_387039845);
		    tmp3 = MULTIPLY(d5, FIX_0_785694958);
		}
	    }
	} else {
	    if (d3) {
		if (d1) {
		    /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
		    z5 = d1 + d3;
		    tmp3 = MULTIPLY(d1, FIX_0_211164243);
		    tmp2 = MULTIPLY(-d3, FIX_1_451774981);
		    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, FIX_0_785694958);
		    tmp1 = MULTIPLY(-d3, FIX_1_387039845);
		    tmp2 = MULTIPLY(-d3, FIX_0_275899380);
		    tmp3 = MULTIPLY(d3, FIX_1_175875602);
		}
	    } else {
		if (d1) {
		    /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
		    tmp0 = MULTIPLY(d1, FIX_0_275899380);
		    tmp1 = MULTIPLY(d1, FIX_0_785694958);
		    tmp2 = MULTIPLY(d1, FIX_1_175875602);
		    tmp3 = MULTIPLY(d1, FIX_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

void
j_rev_dct_sparse(data, pos)
    DCTBLOCK data;
    int pos;
{
  j_rev_dct(data);
}

void
j_rev_dct(data)
    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