    /*
     * 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 */