jrevdct.cpp

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/*
 * 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 <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( 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( 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.
 *
 * Profiling results:
 *  This function only takes about 0.01ms per call, but is called many 
 *  many times, taking about 30% of the total time used by playback.
 *
 *--------------------------------------------------------------
 */

void j_rev_dct( DCTBLOCK data )
{
  INT32 tmp0, tmp1, tmp2, tmp3;
  INT32 tmp10, tmp11, tmp12, tmp13;
  INT32 z1, z2, z3, z4, z5;
  INT32 d0, d1, d2, d3, d4, d5, d6, d7;
  register DCTELEM *dataptr;
  int rowctr;
  SHIFT_TEMPS
   
  /* Pass 1: process rows. */
  /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
  /* furthermore, we scale the results by 2**PASS1_BITS. */

  dataptr = data;

  for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
    /* Due to quantization, we will usually find that many of the input
     * coefficients are zero, especially the AC terms.  We can exploit this