jfdctint.c

/*
 * jfdctint.c
 *
 * This file was part of the Independent JPEG Group's software.
 * Copyright (C) 1991-1996, 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 slow-but-accurate integer implementation of the
 * forward DCT (Discrete Cosine Transform).
 *
 * 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 an algorithm described in
 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
 * The primary algorithm described there uses 11 multiplies and 29 adds.
 * We use their alternate method with 12 multiplies and 32 adds.
 * The advantage of this method is that no data path contains more than one
 * multiplication; this allows a very simple and accurate implementation in
 * scaled fixed-point arithmetic, with a minimal number of shifts.
 */

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

#ifdef DCT_ISLOW_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


/*
 * The poop on this scaling stuff is as follows:
 *
 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
 * larger than the true DCT outputs.  The final outputs are therefore
 * a factor of N larger than desired; since N=8 this can be cured by
 * a simple right shift at the end of the algorithm.  The advantage of
 * this arrangement is that we save two multiplications per 1-D DCT,
 * because the y0 and y4 outputs need not be divided by sqrt(N).
 * In the IJG code, this factor of 8 is removed by the quantization step
 * (in jcdctmgr.c), NOT in this module.
 *
 * We have to do addition and subtraction of the integer inputs, which
 * is no problem, and multiplication by fractional constants, which is
 * a problem to do in integer arithmetic.  We multiply all the constants
 * by CONST_SCALE and convert them to integer constants (thus retaining
 * CONST_BITS bits of precision in the constants).  After doing a
 * multiplication we have to divide the product by CONST_SCALE, with proper
 * rounding, to produce the correct output.  This division can be done
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
 * as long as possible so that partial sums can be added together with
 * full fractional precision.
 *
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
 * they are represented to better-than-integral precision.  These outputs
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
 * with the recommended scaling.  (For 12-bit sample data, the intermediate
 * array is JLONG anyway.)
 *
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
 * shows that the values given below are the most effective.
 */

#if BITS_IN_JSAMPLE == 8
#define CONST_BITS  13
#define PASS1_BITS  2
#else
#define CONST_BITS  13
#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 == 13
#define FIX_0_298631336  ((JLONG)2446)          /* FIX(0.298631336) */
#define FIX_0_390180644  ((JLONG)3196)          /* FIX(0.390180644) */
#define FIX_0_541196100  ((JLONG)4433)          /* FIX(0.541196100) */
#define FIX_0_765366865  ((JLONG)6270)          /* FIX(0.765366865) */
#define FIX_0_899976223  ((JLONG)7373)          /* FIX(0.899976223) */
#define FIX_1_175875602  ((JLONG)9633)          /* FIX(1.175875602) */
#define FIX_1_501321110  ((JLONG)12299)         /* FIX(1.501321110) */
#define FIX_1_847759065  ((JLONG)15137)         /* FIX(1.847759065) */
#define FIX_1_961570560  ((JLONG)16069)         /* FIX(1.961570560) */
#define FIX_2_053119869  ((JLONG)16819)         /* FIX(2.053119869) */
#define FIX_2_562915447  ((JLONG)20995)         /* FIX(2.562915447) */
#define FIX_3_072711026  ((JLONG)25172)         /* FIX(3.072711026) */
#else
#define FIX_0_298631336  FIX(0.298631336)
#define FIX_0_390180644  FIX(0.390180644)
#define FIX_0_541196100  FIX(0.541196100)
#define FIX_0_765366865  FIX(0.765366865)
#define FIX_0_899976223  FIX(0.899976223)
#define FIX_1_175875602  FIX(1.175875602)
#define FIX_1_501321110  FIX(1.501321110)
#define FIX_1_847759065  FIX(1.847759065)
#define FIX_1_961570560  FIX(1.961570560)
#define FIX_2_053119869  FIX(2.053119869)
#define FIX_2_562915447  FIX(2.562915447)
#define FIX_3_072711026  FIX(3.072711026)
#endif


/* Multiply an JLONG variable by an JLONG constant to yield an JLONG result.
 * For 8-bit samples with the recommended scaling, all the variable
 * and constant values involved are no more than 16 bits wide, so a
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 * For 12-bit samples, a full 32-bit multiplication will be needed.
 */

#if BITS_IN_JSAMPLE == 8
#define MULTIPLY(var, const)  MULTIPLY16C16(var, const)
#else
#define MULTIPLY(var, const)  ((var) * (const))
#endif


/*
 * Perform the forward DCT on one block of samples.
 */

GLOBAL(void)
jpeg_fdct_islow(DCTELEM *data)
{
  JLONG tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  JLONG tmp10, tmp11, tmp12, tmp13;
  JLONG z1, z2, z3, z4, z5;
  DCTELEM *dataptr;
  int ctr;
  SHIFT_TEMPS

  /* Pass 1: process rows. */
  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
  /* furthermore, we scale the results by 2**PASS1_BITS. */

  dataptr = data;
  for (ctr = DCTSIZE - 1; ctr >= 0; ctr--) {
    tmp0 = dataptr[0] + dataptr[7];
    tmp7 = dataptr[0] - dataptr[7];
    tmp1 = dataptr[1] + dataptr[6];
    tmp6 = dataptr[1] - dataptr[6];
    tmp2 = dataptr[2] + dataptr[5];
    tmp5 = dataptr[2] - dataptr[5];
    tmp3 = dataptr[3] + dataptr[4];
    tmp4 = dataptr[3] - dataptr[4];

    /* Even part per LL&M figure 1 --- note that published figure is faulty;
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
     */

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

    dataptr[0] = (DCTELEM)LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS);
    dataptr[4] = (DCTELEM)LEFT_SHIFT(tmp10 - tmp11, PASS1_BITS);

    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
    dataptr[2] = (DCTELEM)DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
                                  CONST_BITS - PASS1_BITS);
    dataptr[6] = (DCTELEM)DESCALE(z1 + MULTIPLY(tmp12, -FIX_1_847759065),
                                  CONST_BITS - PASS1_BITS);

    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
     * cK represents cos(K*pi/16).
     * i0..i3 in the paper are tmp4..tmp7 here.
     */

    z1 = tmp4 + tmp7;
    z2 = tmp5 + tmp6;
    z3 = tmp4 + tmp6;
    z4 = tmp5 + tmp7;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, -FIX_0_899976223); /* sqrt(2) * ( c7-c3) */
    z2 = MULTIPLY(z2, -FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, -FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, -FIX_0_390180644); /* sqrt(2) * ( c5-c3) */

    z3 += z5;
    z4 += z5;

    dataptr[7] = (DCTELEM)DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS);
    dataptr[5] = (DCTELEM)DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS);
    dataptr[3] = (DCTELEM)DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS);
    dataptr[1] = (DCTELEM)DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS);

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

  /* Pass 2: process columns.
   * We remove the PASS1_BITS scaling, but leave the results scaled up
   * by an overall factor of 8.
   */

  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 per LL&M figure 1 --- note that published figure is faulty;
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
     */

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

    dataptr[DCTSIZE * 0] = (DCTELEM)DESCALE(tmp10 + tmp11, PASS1_BITS);
    dataptr[DCTSIZE * 4] = (DCTELEM)DESCALE(tmp10 - tmp11, PASS1_BITS);

    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
    dataptr[DCTSIZE * 2] =
      (DCTELEM)DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
                       CONST_BITS + PASS1_BITS);
    dataptr[DCTSIZE * 6] =
      (DCTELEM)DESCALE(z1 + MULTIPLY(tmp12, -FIX_1_847759065),
                       CONST_BITS + PASS1_BITS);

    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
     * cK represents cos(K*pi/16).
     * i0..i3 in the paper are tmp4..tmp7 here.
     */

    z1 = tmp4 + tmp7;
    z2 = tmp5 + tmp6;
    z3 = tmp4 + tmp6;
    z4 = tmp5 + tmp7;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, -FIX_0_899976223); /* sqrt(2) * ( c7-c3) */
    z2 = MULTIPLY(z2, -FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, -FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, -FIX_0_390180644); /* sqrt(2) * ( c5-c3) */

    z3 += z5;
    z4 += z5;

    dataptr[DCTSIZE * 7] = (DCTELEM)DESCALE(tmp4 + z1 + z3,
                                            CONST_BITS + PASS1_BITS);
    dataptr[DCTSIZE * 5] = (DCTELEM)DESCALE(tmp5 + z2 + z4,
                                            CONST_BITS + PASS1_BITS);
    dataptr[DCTSIZE * 3] = (DCTELEM)DESCALE(tmp6 + z2 + z3,
                                            CONST_BITS + PASS1_BITS);
    dataptr[DCTSIZE * 1] = (DCTELEM)DESCALE(tmp7 + z1 + z4,
                                            CONST_BITS + PASS1_BITS);

    dataptr++;                  /* advance pointer to next column */
  }
}

#endif /* DCT_ISLOW_SUPPORTED */