/*

 * jfdctflt.c

 *

 * Copyright (C) 1994-1996, Thomas G. Lane.

 * Modified 2003-2017 by Guido Vollbeding.

 * 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 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).  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 DCT blocks. /* deliberate syntax err */

#endif

/*

 * Perform the forward DCT on one block of samples.

 *

 * cK represents cos(K*pi/16).

 */

GLOBAL(void)

jpeg_fdct_float (FAST_FLOAT * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  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;

  JSAMPROW elemptr;

  int ctr;

  /* Pass 1: process rows. */

  dataptr = data;

  for (ctr = 0; ctr < DCTSIZE; ctr++) {

    elemptr = sample_data[ctr] + start_col;

    /* Load data into workspace */

    tmp0 = (FAST_FLOAT) (GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]));

    tmp7 = (FAST_FLOAT) (GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]));

    tmp1 = (FAST_FLOAT) (GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]));

    tmp6 = (FAST_FLOAT) (GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]));

    tmp2 = (FAST_FLOAT) (GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]));

    tmp5 = (FAST_FLOAT) (GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]));

    tmp3 = (FAST_FLOAT) (GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]));

    tmp4 = (FAST_FLOAT) (GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]));

    /* Even part */

    tmp10 = tmp0 + tmp3;  /* phase 2 */

    tmp13 = tmp0 - tmp3;

    tmp11 = tmp1 + tmp2;

    tmp12 = tmp1 - tmp2;

    /* Apply unsigned->signed conversion. */

    dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* 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 */