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41 results

jrevdct.cpp

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  • jrevdct.cpp 35.90 KiB
    /*
     * 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.
     */
    
    #include <memory.h>
    #include "all.h"
    #include "ansi.h"
    #include "dct.h"
    
    
    #define CONST_BITS 13
    
    /*
     * 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.
     */
    
    /* Actually FIX is no longer used, we precomputed them all */
    #define FIX(x)	((int32) ((x) * CONST_SCALE + 0.5)) 
    
    /* 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
    
    
    /* 
      Unlike our decoder where we approximate the FIXes, we need to use exact
    ones here or successive P-frames will drift too much with Reference frame coding 
    */
    #define FIX_0_211164243 1730
    #define FIX_0_275899380 2260
    #define FIX_0_298631336 2446
    #define FIX_0_390180644 3196
    #define FIX_0_509795579 4176
    #define FIX_0_541196100 4433
    #define FIX_0_601344887 4926
    #define FIX_0_765366865 6270
    #define FIX_0_785694958 6436
    #define FIX_0_899976223 7373
    #define FIX_1_061594337 8697
    #define FIX_1_111140466 9102
    #define FIX_1_175875602 9633
    #define FIX_1_306562965 10703
    #define FIX_1_387039845 11363
    #define FIX_1_451774981 11893
    #define FIX_1_501321110 12299
    #define FIX_1_662939225 13623
    #define FIX_1_847759065 15137
    #define FIX_1_961570560 16069
    #define FIX_2_053119869 16819
    #define FIX_2_172734803 17799
    #define FIX_2_562915447 20995
    #define FIX_3_072711026 25172
    
    /*
      Switch on reverse_dct choices
    */
    void reference_rev_dct _ANSI_ARGS_((int16 *block));
    void mpeg_jrevdct_quick _ANSI_ARGS_((int16 *block));
    void init_idctref _ANSI_ARGS_((void));
    
    extern boolean pureDCT;
    
    void
    mpeg_jrevdct(DCTBLOCK data)
    {
      if (pureDCT) reference_rev_dct(data);
      else mpeg_jrevdct_quick(data);
    }
    
    /*
     * Perform the inverse DCT on one block of coefficients.
     */
    
    void
    mpeg_jrevdct_quick(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 */
      }
    }
    
    
    /* here is the reference one, in case of problems with the normal one */
    
    /* idctref.c, Inverse Discrete Fourier Transform, double precision          */
    
    /* Copyright (C) 1994, MPEG Software Simulation Group. All Rights Reserved. */
    
    /*
     * Disclaimer of Warranty
     *
     * These software programs are available to the user without any license fee or
     * royalty on an "as is" basis.  The MPEG Software Simulation Group disclaims
     * any and all warranties, whether express, implied, or statuary, including any
     * implied warranties or merchantability or of fitness for a particular
     * purpose.  In no event shall the copyright-holder be liable for any
     * incidental, punitive, or consequential damages of any kind whatsoever
     * arising from the use of these programs.
     *
     * This disclaimer of warranty extends to the user of these programs and user's
     * customers, employees, agents, transferees, successors, and assigns.
     *
     * The MPEG Software Simulation Group does not represent or warrant that the
     * programs furnished hereunder are free of infringement of any third-party
     * patents.
     *
     * Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
     * are subject to royalty fees to patent holders.  Many of these patents are
     * general enough such that they are unavoidable regardless of implementation
     * design.
     *
     */
    
    /*  Perform IEEE 1180 reference (64-bit floating point, separable 8x1
     *  direct matrix multiply) Inverse Discrete Cosine Transform
    */
    
    
    /* Here we use math.h to generate constants.  Compiler results may
       vary a little */
    
    #ifndef PI
    #ifdef M_PI
    #define PI M_PI
    #else
    #define PI 3.14159265358979323846
    #endif
    #endif
    
    /* cosine transform matrix for 8x1 IDCT */
    static double itrans_coef[8][8];
    
    /* initialize DCT coefficient matrix */
    
    void init_idctref()
    {
      int freq, time;
      double scale;
    
      for (freq=0; freq < 8; freq++)
      {
        scale = (freq == 0) ? sqrt(0.125) : 0.5;
        for (time=0; time<8; time++)
          itrans_coef[freq][time] = scale*cos((PI/8.0)*freq*(time + 0.5));
      }
    }
    
    /* perform IDCT matrix multiply for 8x8 coefficient block */
    
    void reference_rev_dct(int16 *block)
    {
      int i, j, k, v;
      double partial_product;
      double tmp[64];
    
      for (i=0; i<8; i++)
        for (j=0; j<8; j++)
        {
          partial_product = 0.0;
    
          for (k=0; k<8; k++)
            partial_product+= itrans_coef[k][j]*block[8*i+k];
    
          tmp[8*i+j] = partial_product;
        }
    
      /* Transpose operation is integrated into address mapping by switching 
         loop order of i and j */
    
      for (j=0; j<8; j++)
        for (i=0; i<8; i++)
        {
          partial_product = 0.0;
    
          for (k=0; k<8; k++)
            partial_product+= itrans_coef[k][i]*tmp[8*k+j];
    
          v = (int)floor(partial_product+0.5);
          block[8*i+j] = (v<-256) ? -256 : ((v>255) ? 255 : v);
        }
    }