/*

 * 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, 2020, D. R. Commander.

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

 * file.

 *

 * This file contains a slower but more 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 */