/*

 * jidctflt.c

 *

 * This file was part of the Independent JPEG Group's software:

 * Copyright (C) 1994-1998, Thomas G. Lane.

 * Modified 2010 by Guido Vollbeding.

 * libjpeg-turbo Modifications:

 * Copyright (C) 2014, D. R. Commander.

 * For conditions of distribution and use, see the accompanying README.ijg

 * 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.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

/* 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 = cinfo->sample_range_limit;

  int ctr;

  FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */

#define _0_125  ((FLOAT_MULT_TYPE)0.125)

  /* 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] * _0_125);

      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] * _0_125);

    tmp1 = DEQUANTIZE(inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] * _0_125);

    tmp2 = DEQUANTIZE(inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] * _0_125);

    tmp3 = DEQUANTIZE(inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] * _0_125);

    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] * _0_125);

    tmp5 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] * _0_125);

    tmp6 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] * _0_125);

    tmp7 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] * _0_125);

    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 = z5 - z12 * ((FAST_FLOAT)1.082392200); /* 2*(c2-c6) */

    tmp12 = z5 - z10 * ((FAST_FLOAT)2.613125930); /* 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 * 3] = tmp3 + tmp4;

    wsptr[DCTSIZE * 4] = tmp3 - tmp4;

    inptr++;                    /* advance pointers to next column */

    quantptr++;

    wsptr++;

  }

  /* Pass 2: process rows from work array, store into output array. */

  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 */

    /* Apply signed->unsigned and prepare float->int conversion */

    z5 = wsptr[0] + ((FAST_FLOAT)CENTERJSAMPLE + (FAST_FLOAT)0.5);

    tmp10 = z5 + wsptr[4];

    tmp11 = z5 - 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 = z5 - z12 * ((FAST_FLOAT)1.082392200); /* 2*(c2-c6) */

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

    tmp6 = tmp12 - tmp7;

    tmp5 = tmp11 - tmp6;

    tmp4 = tmp10 - tmp5;

    /* Final output stage: float->int conversion and range-limit */

    outptr[0] = range_limit[((int)(tmp0 + tmp7)) & RANGE_MASK];

    outptr[7] = range_limit[((int)(tmp0 - tmp7)) & RANGE_MASK];

    outptr[1] = range_limit[((int)(tmp1 + tmp6)) & RANGE_MASK];

    outptr[6] = range_limit[((int)(tmp1 - tmp6)) & RANGE_MASK];

    outptr[2] = range_limit[((int)(tmp2 + tmp5)) & RANGE_MASK];

    outptr[5] = range_limit[((int)(tmp2 - tmp5)) & RANGE_MASK];

    outptr[3] = range_limit[((int)(tmp3 + tmp4)) & RANGE_MASK];

    outptr[4] = range_limit[((int)(tmp3 - tmp4)) & RANGE_MASK];

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

  }

}

#endif /* DCT_FLOAT_SUPPORTED */