jfdctflt.c

/*
 * jfdctflt.c
 *
 * Copyright (C) 1994-1996, Thomas G. Lane.
 * This file is part of the Independent JPEG Group's software.
 * For conditions of distribution and use, see the accompanying README.ijg
 * file.
 *
 * This file contains a floating-point implementation of the
 * forward DCT (Discrete Cosine Transform).
 *
 * This implementation should be more accurate than either of the integer
 * DCT implementations.  However, it may not give the same results on all
 * machines because of differences in roundoff behavior.  Speed will depend
 * on the hardware's floating point capacity.
 *
 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
 * 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.
 *
 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
 * JPEG textbook (see REFERENCES section in file README.ijg).  The following
 * code is based directly on figure 4-8 in P&M.
 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
 * possible to arrange the computation so that many of the multiplies are
 * simple scalings of the final outputs.  These multiplies can then be
 * folded into the multiplications or divisions by the JPEG quantization
 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
 * to be done in the DCT itself.
 * The primary disadvantage of this method is that with a fixed-point
 * implementation, accuracy is lost due to imprecise representation of the
 * scaled quantization values.  However, that problem does not arise if
 * we use floating point arithmetic.
 */

#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h"               /* Private declarations for DCT subsystem */

#ifdef DCT_FLOAT_SUPPORTED


/*
 * This module is specialized to the case DCTSIZE = 8.
 */

#if DCTSIZE != 8
  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif


/*
 * Perform the forward DCT on one block of samples.
 */

GLOBAL(void)
jpeg_fdct_float (FAST_FLOAT * data)
{
  FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
  FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
  FAST_FLOAT *dataptr;
  int ctr;

  /* Pass 1: process rows. */

  dataptr = data;
  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
    tmp0 = dataptr[0] + dataptr[7];
    tmp7 = dataptr[0] - dataptr[7];
    tmp1 = dataptr[1] + dataptr[6];
    tmp6 = dataptr[1] - dataptr[6];
    tmp2 = dataptr[2] + dataptr[5];
    tmp5 = dataptr[2] - dataptr[5];
    tmp3 = dataptr[3] + dataptr[4];
    tmp4 = dataptr[3] - dataptr[4];

    /* Even part */

    tmp10 = tmp0 + tmp3;        /* phase 2 */
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;

    dataptr[0] = tmp10 + tmp11; /* phase 3 */
    dataptr[4] = tmp10 - tmp11;

    z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
    dataptr[2] = tmp13 + z1;    /* phase 5 */
    dataptr[6] = tmp13 - z1;

    /* Odd part */

    tmp10 = tmp4 + tmp5;        /* phase 2 */
    tmp11 = tmp5 + tmp6;
    tmp12 = tmp6 + tmp7;

    /* The rotator is modified from fig 4-8 to avoid extra negations. */
    z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
    z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
    z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
    z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */

    z11 = tmp7 + z3;            /* phase 5 */
    z13 = tmp7 - z3;

    dataptr[5] = z13 + z2;      /* phase 6 */
    dataptr[3] = z13 - z2;
    dataptr[1] = z11 + z4;
    dataptr[7] = z11 - z4;

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

  /* Pass 2: process columns. */

  dataptr = data;
  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];

    /* Even part */

    tmp10 = tmp0 + tmp3;        /* phase 2 */
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;

    dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
    dataptr[DCTSIZE*4] = tmp10 - tmp11;

    z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
    dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
    dataptr[DCTSIZE*6] = tmp13 - z1;

    /* Odd part */

    tmp10 = tmp4 + tmp5;        /* phase 2 */
    tmp11 = tmp5 + tmp6;
    tmp12 = tmp6 + tmp7;

    /* The rotator is modified from fig 4-8 to avoid extra negations. */
    z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
    z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
    z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
    z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */

    z11 = tmp7 + z3;            /* phase 5 */
    z13 = tmp7 - z3;

    dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
    dataptr[DCTSIZE*3] = z13 - z2;
    dataptr[DCTSIZE*1] = z11 + z4;
    dataptr[DCTSIZE*7] = z11 - z4;

    dataptr++;                  /* advance pointer to next column */
  }
}

#endif /* DCT_FLOAT_SUPPORTED */