jrevdct.c

/*
 * 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.
 */

#include "jinclude.h"

/*
 * 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 CONST_BITS  13
#define PASS1_BITS  2
#else
#define CONST_BITS  13
#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. */

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

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 * causing a lot of useless floating-point operations at run time.
 * To get around this we use the following pre-calculated constants.
 * If you change CONST_BITS you may want to add appropriate values.
 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 */

#if CONST_BITS == 13
#define FIX_0_298631336  ((INT32)  2446)	/* FIX(0.298631336) */
#define FIX_0_390180644  ((INT32)  3196)	/* FIX(0.390180644) */
#define FIX_0_541196100  ((INT32)  4433)	/* FIX(0.541196100) */
#define FIX_0_765366865  ((INT32)  6270)	/* FIX(0.765366865) */
#define FIX_0_899976223  ((INT32)  7373)	/* FIX(0.899976223) */
#define FIX_1_175875602  ((INT32)  9633)	/* FIX(1.175875602) */
#define FIX_1_501321110  ((INT32)  12299)	/* FIX(1.501321110) */
#define FIX_1_847759065  ((INT32)  15137)	/* FIX(1.847759065) */
#define FIX_1_961570560  ((INT32)  16069)	/* FIX(1.961570560) */
#define FIX_2_053119869  ((INT32)  16819)	/* FIX(2.053119869) */
#define FIX_2_562915447  ((INT32)  20995)	/* FIX(2.562915447) */
#define FIX_3_072711026  ((INT32)  25172)	/* FIX(3.072711026) */
#else
#define FIX_0_298631336  FIX(0.298631336)
#define FIX_0_390180644  FIX(0.390180644)
#define FIX_0_541196100  FIX(0.541196100)
#define FIX_0_765366865  FIX(0.765366865)
#define FIX_0_899976223  FIX(0.899976223)
#define FIX_1_175875602  FIX(1.175875602)
#define FIX_1_501321110  FIX(1.501321110)
#define FIX_1_847759065  FIX(1.847759065)
#define FIX_1_961570560  FIX(1.961570560)
#define FIX_2_053119869  FIX(2.053119869)
#define FIX_2_562915447  FIX(2.562915447)
#define FIX_3_072711026  FIX(3.072711026)
#endif


/* 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


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

GLOBAL void
j_rev_dct (DCTBLOCK data)
{
  INT32 tmp0, tmp1, tmp2, tmp3;
  INT32 tmp10, tmp11, tmp12, tmp13;
  INT32 z1, z2, z3, z4, z5;
  register DCTELEM *dataptr;
  int rowctr;
  SHIFT_TEMPS

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

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

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

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

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

    z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);

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

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

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

    z1 = tmp0 + tmp3;
    z2 = tmp1 + tmp2;
    z3 = tmp0 + tmp2;
    z4 = tmp1 + tmp3;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
    
    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
    
    z3 += z5;
    z4 += z5;
    
    tmp0 += z1 + z3;
    tmp1 += z2 + z4;
    tmp2 += z2 + z3;
    tmp3 += z1 + z4;

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

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

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

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

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

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

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

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

    z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);

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

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

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

    z1 = tmp0 + tmp3;
    z2 = tmp1 + tmp2;
    z3 = tmp0 + tmp2;
    z4 = tmp1 + tmp3;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
    
    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
    
    z3 += z5;
    z4 += z5;
    
    tmp0 += z1 + z3;
    tmp1 += z2 + z4;
    tmp2 += z2 + z3;
    tmp3 += z1 + z4;

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

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