/*

 * jfdctint.c

 *

 * Copyright (C) 1991-1996, Thomas G. Lane.

 * Modification developed 2003-2018 by Guido Vollbeding.

 * 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 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.

 *

 * We also provide FDCT routines with various input sample block sizes for

 * direct resolution reduction or enlargement and for direct resolving the

 * common 2x1 and 1x2 subsampling cases without additional resampling: NxN

 * (N=1...16), 2NxN, and Nx2N (N=1...8) pixels for one 8x8 output DCT block.

 *

 * For N<8 we fill the remaining block coefficients with zero.

 * For N>8 we apply a partial N-point FDCT on the input samples, computing

 * just the lower 8 frequency coefficients and discarding the rest.

 *

 * We must scale the output coefficients of the N-point FDCT appropriately

 * to the standard 8-point FDCT level by 8/N per 1-D pass.  This scaling

 * is folded into the constant multipliers (pass 2) and/or final/initial

 * shifting.

 *

 * CAUTION: We rely on the FIX() macro except for the N=1,2,4,8 cases

 * since there would be too many additional constants to pre-calculate.

 */

#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 DCT blocks. /* 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 INT32 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  ((INT32)  2446)  /* FIX(0.298631336) */

#define FIX_0_390180644  ((INT32)  3196)  /* FIX(0.390180644) */

#define FIX_0_541196100  ((INT32)  4433)  /* FIX(0.541196100) */

#define FIX_0_765366865  ((INT32)  6270)  /* FIX(0.765366865) */

#define FIX_0_899976223  ((INT32)  7373)  /* FIX(0.899976223) */

#define FIX_1_175875602  ((INT32)  9633)  /* FIX(1.175875602) */

#define FIX_1_501321110  ((INT32)  12299) /* FIX(1.501321110) */

#define FIX_1_847759065  ((INT32)  15137) /* FIX(1.847759065) */

#define FIX_1_961570560  ((INT32)  16069) /* FIX(1.961570560) */

#define FIX_2_053119869  ((INT32)  16819) /* FIX(2.053119869) */

#define FIX_2_562915447  ((INT32)  20995) /* FIX(2.562915447) */

#define FIX_3_072711026  ((INT32)  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 INT32 variable by an INT32 constant to yield an INT32 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, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  INT32 tmp0, tmp1, tmp2, tmp3;

  INT32 tmp10, tmp11, tmp12, tmp13;

  INT32 z1;

  DCTELEM *dataptr;

  JSAMPROW elemptr;

  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.

   * cK represents sqrt(2) * cos(K*pi/16).

   */

  dataptr = data;

  for (ctr = 0; ctr < DCTSIZE; ctr++) {

    elemptr = sample_data[ctr] + start_col;

    /* Even part per LL&M figure 1 --- note that published figure is faulty;

     * rotator "c1" should be "c6".

     */

    tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]);

    tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]);

    tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]);

    tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]);

    tmp10 = tmp0 + tmp3;

    tmp12 = tmp0 - tmp3;

    tmp11 = tmp1 + tmp2;

    tmp13 = tmp1 - tmp2;

    tmp0 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]);

    tmp1 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]);

    tmp2 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]);

    tmp3 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]);

    /* Apply unsigned->signed conversion. */

    dataptr[0] = (DCTELEM) ((tmp10 + tmp11 - 8 * CENTERJSAMPLE) << PASS1_BITS);

    dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);

    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);       /* c6 */

    /* Add fudge factor here for final descale. */

    z1 += ONE << (CONST_BITS-PASS1_BITS-1);

    dataptr[2] = (DCTELEM)

      RIGHT_SHIFT(z1 + MULTIPLY(tmp12, FIX_0_765366865), /* c2-c6 */

      CONST_BITS-PASS1_BITS);

    dataptr[6] = (DCTELEM)

      RIGHT_SHIFT(z1 - MULTIPLY(tmp13, FIX_1_847759065), /* c2+c6 */

      CONST_BITS-PASS1_BITS);

    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).

     * i0..i3 in the paper are tmp0..tmp3 here.

     */

    tmp12 = tmp0 + tmp2;

    tmp13 = tmp1 + tmp3;

    z1 = MULTIPLY(tmp12 + tmp13, FIX_1_175875602);       /*  c3 */

    /* Add fudge factor here for final descale. */

    z1 += ONE << (CONST_BITS-PASS1_BITS-1);

    tmp12 = MULTIPLY(tmp12, - FIX_0_390180644);          /* -c3+c5 */

    tmp13 = MULTIPLY(tmp13, - FIX_1_961570560);          /* -c3-c5 */

    tmp12 += z1;

    tmp13 += z1;

    z1 = MULTIPLY(tmp0 + tmp3, - FIX_0_899976223);       /* -c3+c7 */

    tmp0 = MULTIPLY(tmp0, FIX_1_501321110);              /*  c1+c3-c5-c7 */

    tmp3 = MULTIPLY(tmp3, FIX_0_298631336);              /* -c1+c3+c5-c7 */

    tmp0 += z1 + tmp12;

    tmp3 += z1 + tmp13;

    z1 = MULTIPLY(tmp1 + tmp2, - FIX_2_562915447);       /* -c1-c3 */

    tmp1 = MULTIPLY(tmp1, FIX_3_072711026);              /*  c1+c3+c5-c7 */

    tmp2 = MULTIPLY(tmp2, FIX_2_053119869);              /*  c1+c3-c5+c7 */

    tmp1 += z1 + tmp13;

    tmp2 += z1 + tmp12;

    dataptr[1] = (DCTELEM) RIGHT_SHIFT(tmp0, CONST_BITS-PASS1_BITS);

    dataptr[3] = (DCTELEM) RIGHT_SHIFT(tmp1, CONST_BITS-PASS1_BITS);

    dataptr[5] = (DCTELEM) RIGHT_SHIFT(tmp2, CONST_BITS-PASS1_BITS);

    dataptr[7] = (DCTELEM) RIGHT_SHIFT(tmp3, 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.

   * cK represents sqrt(2) * cos(K*pi/16).

   */

  dataptr = data;

  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {

    /* Even part per LL&M figure 1 --- note that published figure is faulty;

     * rotator "c1" should be "c6".

     */

    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];

    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];

    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];

    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];

    /* Add fudge factor here for final descale. */

    tmp10 = tmp0 + tmp3 + (ONE << (PASS1_BITS-1));

    tmp12 = tmp0 - tmp3;

    tmp11 = tmp1 + tmp2;

    tmp13 = tmp1 - tmp2;

    tmp0 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];

    tmp1 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];

    tmp2 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];

    tmp3 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];

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

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

    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);       /* c6 */

    /* Add fudge factor here for final descale. */

    z1 += ONE << (CONST_BITS+PASS1_BITS-1);

    dataptr[DCTSIZE*2] = (DCTELEM)

      RIGHT_SHIFT(z1 + MULTIPLY(tmp12, FIX_0_765366865), /* c2-c6 */

      CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*6] = (DCTELEM)

      RIGHT_SHIFT(z1 - MULTIPLY(tmp13, FIX_1_847759065), /* c2+c6 */

      CONST_BITS+PASS1_BITS);

    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).

     * i0..i3 in the paper are tmp0..tmp3 here.

     */

    tmp12 = tmp0 + tmp2;

    tmp13 = tmp1 + tmp3;

    z1 = MULTIPLY(tmp12 + tmp13, FIX_1_175875602);       /*  c3 */

    /* Add fudge factor here for final descale. */

    z1 += ONE << (CONST_BITS+PASS1_BITS-1);

    tmp12 = MULTIPLY(tmp12, - FIX_0_390180644);          /* -c3+c5 */

    tmp13 = MULTIPLY(tmp13, - FIX_1_961570560);          /* -c3-c5 */

    tmp12 += z1;

    tmp13 += z1;

    z1 = MULTIPLY(tmp0 + tmp3, - FIX_0_899976223);       /* -c3+c7 */

    tmp0 = MULTIPLY(tmp0, FIX_1_501321110);              /*  c1+c3-c5-c7 */

    tmp3 = MULTIPLY(tmp3, FIX_0_298631336);              /* -c1+c3+c5-c7 */

    tmp0 += z1 + tmp12;

    tmp3 += z1 + tmp13;

    z1 = MULTIPLY(tmp1 + tmp2, - FIX_2_562915447);       /* -c1-c3 */

    tmp1 = MULTIPLY(tmp1, FIX_3_072711026);              /*  c1+c3+c5-c7 */

    tmp2 = MULTIPLY(tmp2, FIX_2_053119869);              /*  c1+c3-c5+c7 */

    tmp1 += z1 + tmp13;

    tmp2 += z1 + tmp12;

    dataptr[DCTSIZE*1] = (DCTELEM) RIGHT_SHIFT(tmp0, CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*3] = (DCTELEM) RIGHT_SHIFT(tmp1, CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*5] = (DCTELEM) RIGHT_SHIFT(tmp2, CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*7] = (DCTELEM) RIGHT_SHIFT(tmp3, CONST_BITS+PASS1_BITS);

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

  }

}

#ifdef DCT_SCALING_SUPPORTED

/*

 * Perform the forward DCT on a 7x7 sample block.

 */

GLOBAL(void)

jpeg_fdct_7x7 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  INT32 tmp0, tmp1, tmp2, tmp3;

  INT32 tmp10, tmp11, tmp12;

  INT32 z1, z2, z3;

  DCTELEM *dataptr;

  JSAMPROW elemptr;

  int ctr;

  SHIFT_TEMPS

  /* Pre-zero output coefficient block. */

  MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);

  /* 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.

   * cK represents sqrt(2) * cos(K*pi/14).

   */

  dataptr = data;

  for (ctr = 0; ctr < 7; ctr++) {

    elemptr = sample_data[ctr] + start_col;

    /* Even part */

    tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[6]);

    tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[5]);

    tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[4]);

    tmp3 = GETJSAMPLE(elemptr[3]);

    tmp10 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[6]);

    tmp11 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[5]);

    tmp12 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[4]);

    z1 = tmp0 + tmp2;

    /* Apply unsigned->signed conversion. */

    dataptr[0] = (DCTELEM)

      ((z1 + tmp1 + tmp3 - 7 * CENTERJSAMPLE) << PASS1_BITS);

    tmp3 += tmp3;

    z1 -= tmp3;

    z1 -= tmp3;

    z1 = MULTIPLY(z1, FIX(0.353553391));                /* (c2+c6-c4)/2 */

    z2 = MULTIPLY(tmp0 - tmp2, FIX(0.920609002));       /* (c2+c4-c6)/2 */

    z3 = MULTIPLY(tmp1 - tmp2, FIX(0.314692123));       /* c6 */

    dataptr[2] = (DCTELEM) DESCALE(z1 + z2 + z3, CONST_BITS-PASS1_BITS);

    z1 -= z2;

    z2 = MULTIPLY(tmp0 - tmp1, FIX(0.881747734));       /* c4 */

    dataptr[4] = (DCTELEM)

      DESCALE(z2 + z3 - MULTIPLY(tmp1 - tmp3, FIX(0.707106781)), /* c2+c6-c4 */

        CONST_BITS-PASS1_BITS);

    dataptr[6] = (DCTELEM) DESCALE(z1 + z2, CONST_BITS-PASS1_BITS);

    /* Odd part */

    tmp1 = MULTIPLY(tmp10 + tmp11, FIX(0.935414347));   /* (c3+c1-c5)/2 */

    tmp2 = MULTIPLY(tmp10 - tmp11, FIX(0.170262339));   /* (c3+c5-c1)/2 */

    tmp0 = tmp1 - tmp2;

    tmp1 += tmp2;

    tmp2 = MULTIPLY(tmp11 + tmp12, - FIX(1.378756276)); /* -c1 */

    tmp1 += tmp2;

    tmp3 = MULTIPLY(tmp10 + tmp12, FIX(0.613604268));   /* c5 */

    tmp0 += tmp3;

    tmp2 += tmp3 + MULTIPLY(tmp12, FIX(1.870828693));   /* c3+c1-c5 */

    dataptr[1] = (DCTELEM) DESCALE(tmp0, CONST_BITS-PASS1_BITS);

    dataptr[3] = (DCTELEM) DESCALE(tmp1, CONST_BITS-PASS1_BITS);

    dataptr[5] = (DCTELEM) DESCALE(tmp2, 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.

   * We must also scale the output by (8/7)**2 = 64/49, which we fold

   * into the constant multipliers:

   * cK now represents sqrt(2) * cos(K*pi/14) * 64/49.

   */

  dataptr = data;

  for (ctr = 0; ctr < 7; ctr++) {

    /* Even part */

    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*6];

    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*5];

    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*4];

    tmp3 = dataptr[DCTSIZE*3];

    tmp10 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*6];

    tmp11 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*5];

    tmp12 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*4];

    z1 = tmp0 + tmp2;

    dataptr[DCTSIZE*0] = (DCTELEM)

      DESCALE(MULTIPLY(z1 + tmp1 + tmp3, FIX(1.306122449)), /* 64/49 */

        CONST_BITS+PASS1_BITS);

    tmp3 += tmp3;

    z1 -= tmp3;

    z1 -= tmp3;

    z1 = MULTIPLY(z1, FIX(0.461784020));                /* (c2+c6-c4)/2 */

    z2 = MULTIPLY(tmp0 - tmp2, FIX(1.202428084));       /* (c2+c4-c6)/2 */

    z3 = MULTIPLY(tmp1 - tmp2, FIX(0.411026446));       /* c6 */

    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + z2 + z3, CONST_BITS+PASS1_BITS);

    z1 -= z2;

    z2 = MULTIPLY(tmp0 - tmp1, FIX(1.151670509));       /* c4 */

    dataptr[DCTSIZE*4] = (DCTELEM)

      DESCALE(z2 + z3 - MULTIPLY(tmp1 - tmp3, FIX(0.923568041)), /* c2+c6-c4 */

        CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + z2, CONST_BITS+PASS1_BITS);

    /* Odd part */

    tmp1 = MULTIPLY(tmp10 + tmp11, FIX(1.221765677));   /* (c3+c1-c5)/2 */

    tmp2 = MULTIPLY(tmp10 - tmp11, FIX(0.222383464));   /* (c3+c5-c1)/2 */

    tmp0 = tmp1 - tmp2;

    tmp1 += tmp2;

    tmp2 = MULTIPLY(tmp11 + tmp12, - FIX(1.800824523)); /* -c1 */

    tmp1 += tmp2;

    tmp3 = MULTIPLY(tmp10 + tmp12, FIX(0.801442310));   /* c5 */

    tmp0 += tmp3;

    tmp2 += tmp3 + MULTIPLY(tmp12, FIX(2.443531355));   /* c3+c1-c5 */

    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp0, CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp1, CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp2, CONST_BITS+PASS1_BITS);

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

  }

}

/*

 * Perform the forward DCT on a 6x6 sample block.

 */

GLOBAL(void)

jpeg_fdct_6x6 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  INT32 tmp0, tmp1, tmp2;

  INT32 tmp10, tmp11, tmp12;

  DCTELEM *dataptr;

  JSAMPROW elemptr;

  int ctr;

  SHIFT_TEMPS

  /* Pre-zero output coefficient block. */

  MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);

  /* 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.

   * cK represents sqrt(2) * cos(K*pi/12).

   */

  dataptr = data;

  for (ctr = 0; ctr < 6; ctr++) {

    elemptr = sample_data[ctr] + start_col;

    /* Even part */

    tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[5]);

    tmp11 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[4]);

    tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[3]);

    tmp10 = tmp0 + tmp2;

    tmp12 = tmp0 - tmp2;

    tmp0 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[5]);

    tmp1 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[4]);

    tmp2 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[3]);

    /* Apply unsigned->signed conversion. */

    dataptr[0] = (DCTELEM)

      ((tmp10 + tmp11 - 6 * CENTERJSAMPLE) << PASS1_BITS);

    dataptr[2] = (DCTELEM)

      DESCALE(MULTIPLY(tmp12, FIX(1.224744871)),                 /* c2 */

        CONST_BITS-PASS1_BITS);

    dataptr[4] = (DCTELEM)

      DESCALE(MULTIPLY(tmp10 - tmp11 - tmp11, FIX(0.707106781)), /* c4 */

        CONST_BITS-PASS1_BITS);

    /* Odd part */

    tmp10 = DESCALE(MULTIPLY(tmp0 + tmp2, FIX(0.366025404)),     /* c5 */

        CONST_BITS-PASS1_BITS);

    dataptr[1] = (DCTELEM) (tmp10 + ((tmp0 + tmp1) << PASS1_BITS));

    dataptr[3] = (DCTELEM) ((tmp0 - tmp1 - tmp2) << PASS1_BITS);

    dataptr[5] = (DCTELEM) (tmp10 + ((tmp2 - tmp1) << 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.

   * We must also scale the output by (8/6)**2 = 16/9, which we fold

   * into the constant multipliers:

   * cK now represents sqrt(2) * cos(K*pi/12) * 16/9.

   */

  dataptr = data;

  for (ctr = 0; ctr < 6; ctr++) {

    /* Even part */

    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*5];

    tmp11 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*4];

    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];

    tmp10 = tmp0 + tmp2;

    tmp12 = tmp0 - tmp2;

    tmp0 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*5];

    tmp1 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*4];

    tmp2 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];

    dataptr[DCTSIZE*0] = (DCTELEM)

      DESCALE(MULTIPLY(tmp10 + tmp11, FIX(1.777777778)),         /* 16/9 */

        CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*2] = (DCTELEM)

      DESCALE(MULTIPLY(tmp12, FIX(2.177324216)),                 /* c2 */

        CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*4] = (DCTELEM)

      DESCALE(MULTIPLY(tmp10 - tmp11 - tmp11, FIX(1.257078722)), /* c4 */

        CONST_BITS+PASS1_BITS);

    /* Odd part */

    tmp10 = MULTIPLY(tmp0 + tmp2, FIX(0.650711829));             /* c5 */

    dataptr[DCTSIZE*1] = (DCTELEM)

      DESCALE(tmp10 + MULTIPLY(tmp0 + tmp1, FIX(1.777777778)),   /* 16/9 */

        CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*3] = (DCTELEM)

      DESCALE(MULTIPLY(tmp0 - tmp1 - tmp2, FIX(1.777777778)),    /* 16/9 */

        CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*5] = (DCTELEM)

      DESCALE(tmp10 + MULTIPLY(tmp2 - tmp1, FIX(1.777777778)),   /* 16/9 */

        CONST_BITS+PASS1_BITS);

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

  }

}

/*

 * Perform the forward DCT on a 5x5 sample block.

 */

GLOBAL(void)

jpeg_fdct_5x5 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  INT32 tmp0, tmp1, tmp2;

  INT32 tmp10, tmp11;

  DCTELEM *dataptr;

  JSAMPROW elemptr;

  int ctr;

  SHIFT_TEMPS

  /* Pre-zero output coefficient block. */

  MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);

  /* 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.

   * We scale the results further by 2 as part of output adaption

   * scaling for different DCT size.

   * cK represents sqrt(2) * cos(K*pi/10).

   */

  dataptr = data;

  for (ctr = 0; ctr < 5; ctr++) {

    elemptr = sample_data[ctr] + start_col;

    /* Even part */

    tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[4]);

    tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[3]);

    tmp2 = GETJSAMPLE(elemptr[2]);

    tmp10 = tmp0 + tmp1;

    tmp11 = tmp0 - tmp1;

    tmp0 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[4]);

    tmp1 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[3]);

    /* Apply unsigned->signed conversion. */

    dataptr[0] = (DCTELEM)

      ((tmp10 + tmp2 - 5 * CENTERJSAMPLE) << (PASS1_BITS+1));

    tmp11 = MULTIPLY(tmp11, FIX(0.790569415));          /* (c2+c4)/2 */

    tmp10 -= tmp2 << 2;

    tmp10 = MULTIPLY(tmp10, FIX(0.353553391));          /* (c2-c4)/2 */

    dataptr[2] = (DCTELEM) DESCALE(tmp11 + tmp10, CONST_BITS-PASS1_BITS-1);

    dataptr[4] = (DCTELEM) DESCALE(tmp11 - tmp10, CONST_BITS-PASS1_BITS-1);

    /* Odd part */

    tmp10 = MULTIPLY(tmp0 + tmp1, FIX(0.831253876));    /* c3 */

    dataptr[1] = (DCTELEM)

      DESCALE(tmp10 + MULTIPLY(tmp0, FIX(0.513743148)), /* c1-c3 */

        CONST_BITS-PASS1_BITS-1);

    dataptr[3] = (DCTELEM)

      DESCALE(tmp10 - MULTIPLY(tmp1, FIX(2.176250899)), /* c1+c3 */

        CONST_BITS-PASS1_BITS-1);

    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.

   * We must also scale the output by (8/5)**2 = 64/25, which we partially

   * fold into the constant multipliers (other part was done in pass 1):

   * cK now represents sqrt(2) * cos(K*pi/10) * 32/25.

   */

  dataptr = data;

  for (ctr = 0; ctr < 5; ctr++) {

    /* Even part */

    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*4];

    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*3];

    tmp2 = dataptr[DCTSIZE*2];

    tmp10 = tmp0 + tmp1;

    tmp11 = tmp0 - tmp1;

    tmp0 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*4];

    tmp1 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*3];

    dataptr[DCTSIZE*0] = (DCTELEM)

      DESCALE(MULTIPLY(tmp10 + tmp2, FIX(1.28)),        /* 32/25 */

        CONST_BITS+PASS1_BITS);

    tmp11 = MULTIPLY(tmp11, FIX(1.011928851));          /* (c2+c4)/2 */

    tmp10 -= tmp2 << 2;

    tmp10 = MULTIPLY(tmp10, FIX(0.452548340));          /* (c2-c4)/2 */

    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp11 + tmp10, CONST_BITS+PASS1_BITS);

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

    /* Odd part */

    tmp10 = MULTIPLY(tmp0 + tmp1, FIX(1.064004961));    /* c3 */

    dataptr[DCTSIZE*1] = (DCTELEM)

      DESCALE(tmp10 + MULTIPLY(tmp0, FIX(0.657591230)), /* c1-c3 */

        CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*3] = (DCTELEM)

      DESCALE(tmp10 - MULTIPLY(tmp1, FIX(2.785601151)), /* c1+c3 */

        CONST_BITS+PASS1_BITS);

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

  }

}

/*

 * Perform the forward DCT on a 4x4 sample block.

 */

GLOBAL(void)

jpeg_fdct_4x4 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  INT32 tmp0, tmp1;

  INT32 tmp10, tmp11;

  DCTELEM *dataptr;

  JSAMPROW elemptr;

  int ctr;

  SHIFT_TEMPS

  /* Pre-zero output coefficient block. */

  MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);

  /* 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.

   * We must also scale the output by (8/4)**2 = 2**2, which we add here.

   * cK represents sqrt(2) * cos(K*pi/16) [refers to 8-point FDCT].

   */

  dataptr = data;

  for (ctr = 0; ctr < 4; ctr++) {

    elemptr = sample_data[ctr] + start_col;

    /* Even part */

    tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[3]);

    tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[2]);

    tmp10 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[3]);

    tmp11 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[2]);

    /* Apply unsigned->signed conversion. */

    dataptr[0] = (DCTELEM)

      ((tmp0 + tmp1 - 4 * CENTERJSAMPLE) << (PASS1_BITS+2));

    dataptr[2] = (DCTELEM) ((tmp0 - tmp1) << (PASS1_BITS+2));

    /* Odd part */

    tmp0 = MULTIPLY(tmp10 + tmp11, FIX_0_541196100);       /* c6 */

    /* Add fudge factor here for final descale. */

    tmp0 += ONE << (CONST_BITS-PASS1_BITS-3);

    dataptr[1] = (DCTELEM)

      RIGHT_SHIFT(tmp0 + MULTIPLY(tmp10, FIX_0_765366865), /* c2-c6 */

      CONST_BITS-PASS1_BITS-2);

    dataptr[3] = (DCTELEM)

      RIGHT_SHIFT(tmp0 - MULTIPLY(tmp11, FIX_1_847759065), /* c2+c6 */

      CONST_BITS-PASS1_BITS-2);

    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.

   * cK represents sqrt(2) * cos(K*pi/16) [refers to 8-point FDCT].

   */

  dataptr = data;

  for (ctr = 0; ctr < 4; ctr++) {

    /* Even part */

    /* Add fudge factor here for final descale. */

    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*3] + (ONE << (PASS1_BITS-1));

    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*2];

    tmp10 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*3];

    tmp11 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*2];

    dataptr[DCTSIZE*0] = (DCTELEM) RIGHT_SHIFT(tmp0 + tmp1, PASS1_BITS);

    dataptr[DCTSIZE*2] = (DCTELEM) RIGHT_SHIFT(tmp0 - tmp1, PASS1_BITS);

    /* Odd part */

    tmp0 = MULTIPLY(tmp10 + tmp11, FIX_0_541196100);       /* c6 */

    /* Add fudge factor here for final descale. */

    tmp0 += ONE << (CONST_BITS+PASS1_BITS-1);

    dataptr[DCTSIZE*1] = (DCTELEM)

      RIGHT_SHIFT(tmp0 + MULTIPLY(tmp10, FIX_0_765366865), /* c2-c6 */

      CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*3] = (DCTELEM)

      RIGHT_SHIFT(tmp0 - MULTIPLY(tmp11, FIX_1_847759065), /* c2+c6 */

      CONST_BITS+PASS1_BITS);

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

  }

}

/*

 * Perform the forward DCT on a 3x3 sample block.

 */

GLOBAL(void)

jpeg_fdct_3x3 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  INT32 tmp0, tmp1, tmp2;

  DCTELEM *dataptr;

  JSAMPROW elemptr;

  int ctr;

  SHIFT_TEMPS

  /* Pre-zero output coefficient block. */

  MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);

  /* 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.

   * We scale the results further by 2**2 as part of output adaption

   * scaling for different DCT size.

   * cK represents sqrt(2) * cos(K*pi/6).

   */

  dataptr = data;

  for (ctr = 0; ctr < 3; ctr++) {

    elemptr = sample_data[ctr] + start_col;

    /* Even part */

    tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[2]);

    tmp1 = GETJSAMPLE(elemptr[1]);

    tmp2 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[2]);

    /* Apply unsigned->signed conversion. */

    dataptr[0] = (DCTELEM)

      ((tmp0 + tmp1 - 3 * CENTERJSAMPLE) << (PASS1_BITS+2));

    dataptr[2] = (DCTELEM)

      DESCALE(MULTIPLY(tmp0 - tmp1 - tmp1, FIX(0.707106781)), /* c2 */

        CONST_BITS-PASS1_BITS-2);

    /* Odd part */

    dataptr[1] = (DCTELEM)

      DESCALE(MULTIPLY(tmp2, FIX(1.224744871)),               /* c1 */

        CONST_BITS-PASS1_BITS-2);

    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.

   * We must also scale the output by (8/3)**2 = 64/9, which we partially

   * fold into the constant multipliers (other part was done in pass 1):

   * cK now represents sqrt(2) * cos(K*pi/6) * 16/9.

   */

  dataptr = data;

  for (ctr = 0; ctr < 3; ctr++) {

    /* Even part */

    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*2];

    tmp1 = dataptr[DCTSIZE*1];

    tmp2 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*2];

    dataptr[DCTSIZE*0] = (DCTELEM)

      DESCALE(MULTIPLY(tmp0 + tmp1, FIX(1.777777778)),        /* 16/9 */

        CONST_BITS+PASS1_BITS);

    dataptr[DCTSIZE*2] = (DCTELEM)

      DESCALE(MULTIPLY(tmp0 - tmp1 - tmp1, FIX(1.257078722)), /* c2 */

        CONST_BITS+PASS1_BITS);

    /* Odd part */

    dataptr[DCTSIZE*1] = (DCTELEM)

      DESCALE(MULTIPLY(tmp2, FIX(2.177324216)),               /* c1 */

        CONST_BITS+PASS1_BITS);

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

  }

}

/*

 * Perform the forward DCT on a 2x2 sample block.

 */

GLOBAL(void)

jpeg_fdct_2x2 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  DCTELEM tmp0, tmp1, tmp2, tmp3;

  JSAMPROW elemptr;

  /* Pre-zero output coefficient block. */

  MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);

  /* Pass 1: process rows.

   * Note results are scaled up by sqrt(8) compared to a true DCT.

   */

  /* Row 0 */

  elemptr = sample_data[0] + start_col;

  tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[1]);

  tmp1 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[1]);

  /* Row 1 */

  elemptr = sample_data[1] + start_col;

  tmp2 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[1]);

  tmp3 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[1]);

  /* Pass 2: process columns.

   * We leave the results scaled up by an overall factor of 8.

   * We must also scale the output by (8/2)**2 = 2**4.

   */

  /* Column 0 */

  /* Apply unsigned->signed conversion. */

  data[DCTSIZE*0] = (tmp0 + tmp2 - 4 * CENTERJSAMPLE) << 4;

  data[DCTSIZE*1] = (tmp0 - tmp2) << 4;

  /* Column 1 */

  data[DCTSIZE*0+1] = (tmp1 + tmp3) << 4;

  data[DCTSIZE*1+1] = (tmp1 - tmp3) << 4;

}

/*

 * Perform the forward DCT on a 1x1 sample block.

 */

GLOBAL(void)

jpeg_fdct_1x1 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{

  DCTELEM dcval;

  /* Pre-zero output coefficient block. */

  MEMZERO(data, SIZEOF(DCTELEM) * DCTSIZE2);

  dcval = GETJSAMPLE(sample_data[0][start_col]);

  /* We leave the result scaled up by an overall factor of 8. */

  /* We must also scale the output by (8/1)**2 = 2**6. */

  /* Apply unsigned->signed conversion. */

  data[0] = (dcval - CENTERJSAMPLE) << 6;

}

/*

 * Perform the forward DCT on a 9x9 sample block.

 */

GLOBAL(void)

jpeg_fdct_9x9 (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)

{