/*

 * This file is part of the Independent JPEG Group's software.

 *

 * The authors make NO WARRANTY or representation, either express or implied,

 * with respect to this software, its quality, accuracy, merchantability, or

 * fitness for a particular purpose.  This software is provided "AS IS", and

 * you, its user, assume the entire risk as to its quality and accuracy.

 *

 * This software is copyright (C) 1991-1996, Thomas G. Lane.

 * All Rights Reserved except as specified below.

 *

 * Permission is hereby granted to use, copy, modify, and distribute this

 * software (or portions thereof) for any purpose, without fee, subject to

 * these conditions:

 * (1) If any part of the source code for this software is distributed, then

 * this README file must be included, with this copyright and no-warranty

 * notice unaltered; and any additions, deletions, or changes to the original

 * files must be clearly indicated in accompanying documentation.

 * (2) If only executable code is distributed, then the accompanying

 * documentation must state that "this software is based in part on the work

 * of the Independent JPEG Group".

 * (3) Permission for use of this software is granted only if the user accepts

 * full responsibility for any undesirable consequences; the authors accept

 * NO LIABILITY for damages of any kind.

 *

 * These conditions apply to any software derived from or based on the IJG

 * code, not just to the unmodified library.  If you use our work, you ought

 * to acknowledge us.

 *

 * Permission is NOT granted for the use of any IJG author's name or company

 * name in advertising or publicity relating to this software or products

 * derived from it.  This software may be referred to only as "the Independent

 * JPEG Group's software".

 *

 * We specifically permit and encourage the use of this software as the basis

 * of commercial products, provided that all warranty or liability claims are

 * assumed by the product vendor.

 *

 * 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.

 */

/**

 * @file

 * Independent JPEG Group's slow & accurate dct.

 */

#include "libavutil/common.h"

#include "dct.h"

#include "bit_depth_template.c"

#define DCTSIZE 8

#define BITS_IN_JSAMPLE BIT_DEPTH

#define GLOBAL(x) x

#define RIGHT_SHIFT(x, n) ((x) >> (n))

#define MULTIPLY16C16(var,const) ((var)*(const))

#define DESCALE(x,n)  RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)

/*

 * This module is specialized to the case DCTSIZE = 8.

 */

#if DCTSIZE != 8

#error  "Sorry, this code only copes with 8x8 DCTs."

#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_t 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.

 */

#undef CONST_BITS

#undef PASS1_BITS

#undef OUT_SHIFT

#if BITS_IN_JSAMPLE == 8

#define CONST_BITS  13

#define PASS1_BITS  4   /* set this to 2 if 16x16 multiplies are faster */

#define OUT_SHIFT   PASS1_BITS

#else

#define CONST_BITS  13

#define PASS1_BITS  1   /* lose a little precision to avoid overflow */

#define OUT_SHIFT   (PASS1_BITS + 1)

#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_t)  2446)      /* FIX(0.298631336) */

#define FIX_0_390180644  ((int32_t)  3196)      /* FIX(0.390180644) */

#define FIX_0_541196100  ((int32_t)  4433)      /* FIX(0.541196100) */

#define FIX_0_765366865  ((int32_t)  6270)      /* FIX(0.765366865) */

#define FIX_0_899976223  ((int32_t)  7373)      /* FIX(0.899976223) */

#define FIX_1_175875602  ((int32_t)  9633)      /* FIX(1.175875602) */

#define FIX_1_501321110  ((int32_t)  12299)     /* FIX(1.501321110) */

#define FIX_1_847759065  ((int32_t)  15137)     /* FIX(1.847759065) */

#define FIX_1_961570560  ((int32_t)  16069)     /* FIX(1.961570560) */

#define FIX_2_053119869  ((int32_t)  16819)     /* FIX(2.053119869) */

#define FIX_2_562915447  ((int32_t)  20995)     /* FIX(2.562915447) */

#define FIX_3_072711026  ((int32_t)  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_t variable by an int32_t constant to yield an int32_t 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 && CONST_BITS<=13 && PASS1_BITS<=2

#define MULTIPLY(var,const)  MULTIPLY16C16(var,const)

#else

#define MULTIPLY(var,const)  ((var) * (const))

#endif

{

  int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  int tmp10, tmp11, tmp12, tmp13;

  int z1, z2, z3, z4, z5;

  int16_t *dataptr;

  int ctr;

  /* 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. */

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

     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".

     */

                                   CONST_BITS-PASS1_BITS);

                                   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.

     */

  }

/*

 * Perform the forward DCT on one block of samples.

 */

GLOBAL(void)

{

  int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  int tmp10, tmp11, tmp12, tmp13;

  int z1, z2, z3, z4, z5;

  int16_t *dataptr;

  int ctr;

  /* Pass 2: process columns.

   * We remove the PASS1_BITS scaling, but leave the results scaled up

   * by an overall factor of 8.

   */

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

     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".

     */

                                 CONST_BITS + OUT_SHIFT);

                                 CONST_BITS + OUT_SHIFT);

    /* 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.

     */

  }

/*

 * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT

 * on the rows and then, instead of doing even and odd, part on the columns

 * you do even part two times.

 */

GLOBAL(void)

{

  int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  int tmp10, tmp11, tmp12, tmp13;

  int z1;

  int16_t *dataptr;

  int ctr;

  /* Pass 2: process columns.

   * We remove the PASS1_BITS scaling, but leave the results scaled up

   * by an overall factor of 8.

   */

                                  CONST_BITS+OUT_SHIFT);

                                  CONST_BITS+OUT_SHIFT);

                                  CONST_BITS + OUT_SHIFT);

                                  CONST_BITS + OUT_SHIFT);

  }

}