File: jidctfst.c

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/*
 * jidctfst.c
 *
 * This file was part of the Independent JPEG Group's software:
 * Copyright (C) 1994-1998, Thomas G. Lane.
 * libjpeg-turbo Modifications:
 * Copyright (C) 2015, D. R. Commander.
 * For conditions of distribution and use, see the accompanying README.ijg
 * file.
 *
 * This file contains a fast, not so accurate integer implementation of the
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
 * must also perform dequantization of the input coefficients.
 *
 * 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 fixed-point math,
 * accuracy is lost due to imprecise representation of the scaled
 * quantization values.  The smaller the quantization table entry, the less
 * precise the scaled value, so this implementation does worse with high-
 * quality-setting files than with low-quality ones.
 */

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

#ifdef DCT_IFAST_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


/* Scaling decisions are generally the same as in the LL&M algorithm;
 * see jidctint.c for more details.  However, we choose to descale
 * (right shift) multiplication products as soon as they are formed,
 * rather than carrying additional fractional bits into subsequent additions.
 * This compromises accuracy slightly, but it lets us save a few shifts.
 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
 * everywhere except in the multiplications proper; this saves a good deal
 * of work on 16-bit-int machines.
 *
 * The dequantized coefficients are not integers because the AA&N scaling
 * factors have been incorporated.  We represent them scaled up by PASS1_BITS,
 * so that the first and second IDCT rounds have the same input scaling.
 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
 * avoid a descaling shift; this compromises accuracy rather drastically
 * for small quantization table entries, but it saves a lot of shifts.
 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
 * so we use a much larger scaling factor to preserve accuracy.
 *
 * A final compromise is to represent the multiplicative constants to only
 * 8 fractional bits, rather than 13.  This saves some shifting work on some
 * machines, and may also reduce the cost of multiplication (since there
 * are fewer one-bits in the constants).
 */

#if BITS_IN_JSAMPLE == 8
#define CONST_BITS  8
#define PASS1_BITS  2
#else
#define CONST_BITS  8
#define PASS1_BITS  1           /* lose a little precision to avoid overflow */
#endif

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 * causing a lot of useless floating-point operations at run time.
 * To get around this we use the following pre-calculated constants.
 * If you change CONST_BITS you may want to add appropriate values.
 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 */

#if CONST_BITS == 8
#define FIX_1_082392200  ((JLONG)  277)         /* FIX(1.082392200) */
#define FIX_1_414213562  ((JLONG)  362)         /* FIX(1.414213562) */
#define FIX_1_847759065  ((JLONG)  473)         /* FIX(1.847759065) */
#define FIX_2_613125930  ((JLONG)  669)         /* FIX(2.613125930) */
#else
#define FIX_1_082392200  FIX(1.082392200)
#define FIX_1_414213562  FIX(1.414213562)
#define FIX_1_847759065  FIX(1.847759065)
#define FIX_2_613125930  FIX(2.613125930)
#endif


/* We can gain a little more speed, with a further compromise in accuracy,
 * by omitting the addition in a descaling shift.  This yields an incorrectly
 * rounded result half the time...
 */

#ifndef USE_ACCURATE_ROUNDING
#undef DESCALE
#define DESCALE(x,n)  RIGHT_SHIFT(x, n)
#endif


/* Multiply a DCTELEM variable by an JLONG constant, and immediately
 * descale to yield a DCTELEM result.
 */

#define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))


/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce a DCTELEM result.  For 8-bit data a 16x16->16
 * multiplication will do.  For 12-bit data, the multiplier table is
 * declared JLONG, so a 32-bit multiply will be used.
 */

#if BITS_IN_JSAMPLE == 8
#define DEQUANTIZE(coef,quantval)  (((IFAST_MULT_TYPE) (coef)) * (quantval))
#else
#define DEQUANTIZE(coef,quantval)  \
        DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
#endif


/* Like DESCALE, but applies to a DCTELEM and produces an int.
 * We assume that int right shift is unsigned if JLONG right shift is.
 */

#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define ISHIFT_TEMPS    DCTELEM ishift_temp;
#if BITS_IN_JSAMPLE == 8
#define DCTELEMBITS  16         /* DCTELEM may be 16 or 32 bits */
#else
#define DCTELEMBITS  32         /* DCTELEM must be 32 bits */
#endif
#define IRIGHT_SHIFT(x,shft)  \
    ((ishift_temp = (x)) < 0 ? \
     (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
     (ishift_temp >> (shft)))
#else
#define ISHIFT_TEMPS
#define IRIGHT_SHIFT(x,shft)    ((x) >> (shft))
#endif

#ifdef USE_ACCURATE_ROUNDING
#define IDESCALE(x,n)  ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
#else
#define IDESCALE(x,n)  ((int) IRIGHT_SHIFT(x, n))
#endif


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

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

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

  inptr = coef_block;
  quantptr = (IFAST_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 */
      int dcval = (int) 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 = MULTIPLY(tmp1 - tmp3, FIX_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 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */

    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
    tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
    tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */

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

    wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
    wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
    wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
    wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
    wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
    wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
    wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
    wsptr[DCTSIZE*3] = (int) (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, */
  /* and also undo the PASS1_BITS scaling. */

  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).
     * On machines with very fast multiplication, it's possible that the
     * test takes more time than it's worth.  In that case this section
     * may be commented out.
     */

#ifndef NO_ZERO_ROW_TEST
    if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
        wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
      /* AC terms all zero */
      JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
                                  & RANGE_MASK];

      outptr[0] = dcval;
      outptr[1] = dcval;
      outptr[2] = dcval;
      outptr[3] = dcval;
      outptr[4] = dcval;
      outptr[5] = dcval;
      outptr[6] = dcval;
      outptr[7] = dcval;

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

    /* Even part */

    tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
    tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);

    tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
    tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
            - tmp13;

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

    /* Odd part */

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

    tmp7 = z11 + z13;           /* phase 5 */
    tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */

    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
    tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
    tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */

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

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

    outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
                            & RANGE_MASK];
    outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
                            & RANGE_MASK];
    outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
                            & RANGE_MASK];
    outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
                            & RANGE_MASK];
    outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
                            & RANGE_MASK];
    outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
                            & RANGE_MASK];
    outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
                            & RANGE_MASK];
    outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
                            & RANGE_MASK];

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

#endif /* DCT_IFAST_SUPPORTED */