    /*
     * jidctflt.c
     *
     * Copyright (C) 1994-1998, 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 a floating-point implementation of the
     * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
     * must also perform dequantization of the input coefficients.
     *
     * This implementation should be more accurate than either of the integer
     * IDCT 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 IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
     * on each row (or vice versa, but it's more convenient to emit a row at
     * a time).  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 DCTs. /* deliberate syntax err */
    #endif

    /* Dequantize a coefficient by multiplying it by the multiplier-table
     * entry; produce a float result.
     */

    #define DEQUANTIZE(coef,quantval)  (((FAST_FLOAT) (coef)) * (quantval))

    /*
     * Perform dequantization and inverse DCT on one block of coefficients.
     */

    GLOBAL(void)
    jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
    		 JCOEFPTR coef_block,
    		 JSAMPARRAY output_buf, JDIMENSION output_col)
    {
      FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
      FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
      FAST_FLOAT z5, z10, z11, z12, z13;
      JCOEFPTR inptr;
      FLOAT_MULT_TYPE * quantptr;
      FAST_FLOAT * wsptr;
      JSAMPROW outptr;
      JSAMPLE *range_limit = IDCT_range_limit(cinfo);
      int ctr;
      FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
      SHIFT_TEMPS

      /* Pass 1: process columns from input, store into work array. */

      inptr = coef_block;
      quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
      wsptr = workspace;
      for (ctr = DCTSIZE; ctr > 0; ctr--) {
        /* 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 column 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
         * column DCT calculations can be simplified this way.
         */

        if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
    	inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
    	inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
    	inptr[DCTSIZE*7] == 0) {
          /* AC terms all zero */
          FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

          wsptr[DCTSIZE*0] = dcval;
          wsptr[DCTSIZE*1] = dcval;
          wsptr[DCTSIZE*2] = dcval;
          wsptr[DCTSIZE*3] = dcval;
          wsptr[DCTSIZE*4] = dcval;
          wsptr[DCTSIZE*5] = dcval;
          wsptr[DCTSIZE*6] = dcval;
          wsptr[DCTSIZE*7] = dcval;

          inptr++;			/* advance pointers to next column */
          quantptr++;
          wsptr++;
          continue;
        }

        /* Even part */

        tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
        tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
        tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
        tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

        tmp10 = tmp0 + tmp2;	/* phase 3 */
        tmp11 = tmp0 - tmp2;

        tmp13 = tmp1 + tmp3;	/* phases 5-3 */
        tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */

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

        /* Odd part */

        tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
        tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
        tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
        tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);

        z13 = tmp6 + tmp5;		/* phase 6 */
        z10 = tmp6 - tmp5;
        z11 = tmp4 + tmp7;
        z12 = tmp4 - tmp7;

        tmp7 = z11 + z13;		/* phase 5 */
        tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */

        z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
        tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
        tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */

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

        wsptr[DCTSIZE*0] = tmp0 + tmp7;
        wsptr[DCTSIZE*7] = tmp0 - tmp7;
        wsptr[DCTSIZE*1] = tmp1 + tmp6;
        wsptr[DCTSIZE*6] = tmp1 - tmp6;
        wsptr[DCTSIZE*2] = tmp2 + tmp5;
        wsptr[DCTSIZE*5] = tmp2 - tmp5;
        wsptr[DCTSIZE*4] = tmp3 + tmp4;
        wsptr[DCTSIZE*3] = tmp3 - tmp4;

        inptr++;			/* advance pointers to next column */
        quantptr++;
        wsptr++;
      }

      /* Pass 2: process rows from work array, store into output array. */
      /* Note that we must descale the results by a factor of 8 == 2**3. */

      wsptr = workspace;
      for (ctr = 0; ctr < DCTSIZE; ctr++) {
        outptr = output_buf[ctr] + output_col;
        /* Rows of zeroes can be exploited in the same way as we did with columns.
         * However, the column calculation has created many nonzero AC terms, so
         * the simplification applies less often (typically 5% to 10% of the time).
         * And testing floats for zero is relatively expensive, so we don't bother.
         */

        /* Even part */

        tmp10 = wsptr[0] + wsptr[4];
        tmp11 = wsptr[0] - wsptr[4];

        tmp13 = wsptr[2] + wsptr[6];
        tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;

        tmp0 = tmp10 + tmp13;
        tmp3 = tmp10 - tmp13;
        tmp1 = tmp11 + tmp12;
        tmp2 = tmp11 - tmp12;

        /* Odd part */

        z13 = wsptr[5] + wsptr[3];
        z10 = wsptr[5] - wsptr[3];
        z11 = wsptr[1] + wsptr[7];
        z12 = wsptr[1] - wsptr[7];

        tmp7 = z11 + z13;
        tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);

        z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
        tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
        tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */

        tmp6 = tmp12 - tmp7;
        tmp5 = tmp11 - tmp6;
        tmp4 = tmp10 + tmp5;

        /* Final output stage: scale down by a factor of 8 and range-limit */

        outptr[0] = range_limit[(int) DESCALE((long) (tmp0 + tmp7), 3)
    			    & RANGE_MASK];
        outptr[7] = range_limit[(int) DESCALE((long) (tmp0 - tmp7), 3)
    			    & RANGE_MASK];
        outptr[1] = range_limit[(int) DESCALE((long) (tmp1 + tmp6), 3)
    			    & RANGE_MASK];
        outptr[6] = range_limit[(int) DESCALE((long) (tmp1 - tmp6), 3)
    			    & RANGE_MASK];
        outptr[2] = range_limit[(int) DESCALE((long) (tmp2 + tmp5), 3)
    			    & RANGE_MASK];
        outptr[5] = range_limit[(int) DESCALE((long) (tmp2 - tmp5), 3)
    			    & RANGE_MASK];
        outptr[4] = range_limit[(int) DESCALE((long) (tmp3 + tmp4), 3)
    			    & RANGE_MASK];
        outptr[3] = range_limit[(int) DESCALE((long) (tmp3 - tmp4), 3)
    			    & RANGE_MASK];

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

    #endif /* DCT_FLOAT_SUPPORTED */