/*****************************************************************************
*
* XVID MPEG-4 VIDEO CODEC
* - fast disrete cosine transformation - integer C version
*
* These routines are from Independent JPEG Group's free JPEG software
* Copyright (C) 1991-1998, Thomas G. Lane (see the file README.IJG)
*
* This file is part of XviD, a free MPEG-4 video encoder/decoder
*
* XviD is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* Under section 8 of the GNU General Public License, the copyright
* holders of XVID explicitly forbid distribution in the following
* countries:
*
* - Japan
* - United States of America
*
* Linking XviD statically or dynamically with other modules is making a
* combined work based on XviD. Thus, the terms and conditions of the
* GNU General Public License cover the whole combination.
*
* As a special exception, the copyright holders of XviD give you
* permission to link XviD with independent modules that communicate with
* XviD solely through the VFW1.1 and DShow interfaces, regardless of the
* license terms of these independent modules, and to copy and distribute
* the resulting combined work under terms of your choice, provided that
* every copy of the combined work is accompanied by a complete copy of
* the source code of XviD (the version of XviD used to produce the
* combined work), being distributed under the terms of the GNU General
* Public License plus this exception. An independent module is a module
* which is not derived from or based on XviD.
*
* Note that people who make modified versions of XviD are not obligated
* to grant this special exception for their modified versions; it is
* their choice whether to do so. The GNU General Public License gives
* permission to release a modified version without this exception; this
* exception also makes it possible to release a modified version which
* carries forward this exception.
*
* $Id: fdct.c,v 1.4 2002/11/16 23:51:58 edgomez Exp $
*
*************************************************************************/
/* This routine is a slow-but-accurate integer implementation of the
* forward DCT (Discrete Cosine Transform). Taken from the IJG software
*
* 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.
*
* 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), here it is removed.
*
* 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 8 + 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 8 + CONST_BITS + PASS1_BITS <= 26. Error analysis
* shows that the values given below are the most effective.
*
* 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...
*/
#include "fdct.h"
#define USE_ACCURATE_ROUNDING
#define RIGHT_SHIFT(x, shft) ((x) >> (shft))
#ifdef USE_ACCURATE_ROUNDING
#define ONE ((int) 1)
#define DESCALE(x, n) RIGHT_SHIFT((x) + (ONE << ((n) - 1)), n)
#else
#define DESCALE(x, n) RIGHT_SHIFT(x, n)
#endif
#define CONST_BITS 13
#define PASS1_BITS 2
#define FIX_0_298631336 ((int) 2446) /* FIX(0.298631336) */
#define FIX_0_390180644 ((int) 3196) /* FIX(0.390180644) */
#define FIX_0_541196100 ((int) 4433) /* FIX(0.541196100) */
#define FIX_0_765366865 ((int) 6270) /* FIX(0.765366865) */
#define FIX_0_899976223 ((int) 7373) /* FIX(0.899976223) */
#define FIX_1_175875602 ((int) 9633) /* FIX(1.175875602) */
#define FIX_1_501321110 ((int) 12299) /* FIX(1.501321110) */
#define FIX_1_847759065 ((int) 15137) /* FIX(1.847759065) */
#define FIX_1_961570560 ((int) 16069) /* FIX(1.961570560) */
#define FIX_2_053119869 ((int) 16819) /* FIX(2.053119869) */
#define FIX_2_562915447 ((int) 20995) /* FIX(2.562915447) */
#define FIX_3_072711026 ((int) 25172) /* FIX(3.072711026) */
// function pointer
fdctFuncPtr fdct;
/*
* Perform an integer forward DCT on one block of samples.
*/
void
fdct_int32(short *const block)
{
int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
int tmp10, tmp11, tmp12, tmp13;
int z1, z2, z3, z4, z5;
short *blkptr;
int *dataptr;
int data[64];
int i;
/* 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;
blkptr = block;
for (i = 0; i < 8; i++) {
tmp0 = blkptr[0] + blkptr[7];
tmp7 = blkptr[0] - blkptr[7];
tmp1 = blkptr[1] + blkptr[6];
tmp6 = blkptr[1] - blkptr[6];
tmp2 = blkptr[2] + blkptr[5];
tmp5 = blkptr[2] - blkptr[5];
tmp3 = blkptr[3] + blkptr[4];
tmp4 = blkptr[3] - blkptr[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] = (tmp10 + tmp11) << PASS1_BITS;
dataptr[4] = (tmp10 - tmp11) << PASS1_BITS;
z1 = (tmp12 + tmp13) * FIX_0_541196100;
dataptr[2] =
DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS - PASS1_BITS);
dataptr[6] =
DESCALE(z1 + 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 = (z3 + z4) * FIX_1_175875602; /* sqrt(2) * c3 */
tmp4 *= FIX_0_298631336; /* sqrt(2) * (-c1+c3+c5-c7) */
tmp5 *= FIX_2_053119869; /* sqrt(2) * ( c1+c3-c5+c7) */
tmp6 *= FIX_3_072711026; /* sqrt(2) * ( c1+c3+c5-c7) */
tmp7 *= FIX_1_501321110; /* sqrt(2) * ( c1+c3-c5-c7) */
z1 *= -FIX_0_899976223; /* sqrt(2) * (c7-c3) */
z2 *= -FIX_2_562915447; /* sqrt(2) * (-c1-c3) */
z3 *= -FIX_1_961570560; /* sqrt(2) * (-c3-c5) */
z4 *= -FIX_0_390180644; /* sqrt(2) * (c5-c3) */
z3 += z5;
z4 += z5;
dataptr[7] = DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS);
dataptr[5] = DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS);
dataptr[3] = DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS);
dataptr[1] = DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS);
dataptr += 8; /* advance pointer to next row */
blkptr += 8;
}
/* 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 (i = 0; i < 8; i++) {
tmp0 = dataptr[0] + dataptr[56];
tmp7 = dataptr[0] - dataptr[56];
tmp1 = dataptr[8] + dataptr[48];
tmp6 = dataptr[8] - dataptr[48];
tmp2 = dataptr[16] + dataptr[40];
tmp5 = dataptr[16] - dataptr[40];
tmp3 = dataptr[24] + dataptr[32];
tmp4 = dataptr[24] - dataptr[32];
/* 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] = DESCALE(tmp10 + tmp11, PASS1_BITS);
dataptr[32] = DESCALE(tmp10 - tmp11, PASS1_BITS);
z1 = (tmp12 + tmp13) * FIX_0_541196100;
dataptr[16] =
DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS + PASS1_BITS);
dataptr[48] =
DESCALE(z1 + 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 = (z3 + z4) * FIX_1_175875602; /* sqrt(2) * c3 */
tmp4 *= FIX_0_298631336; /* sqrt(2) * (-c1+c3+c5-c7) */
tmp5 *= FIX_2_053119869; /* sqrt(2) * ( c1+c3-c5+c7) */
tmp6 *= FIX_3_072711026; /* sqrt(2) * ( c1+c3+c5-c7) */
tmp7 *= FIX_1_501321110; /* sqrt(2) * ( c1+c3-c5-c7) */
z1 *= -FIX_0_899976223; /* sqrt(2) * (c7-c3) */
z2 *= -FIX_2_562915447; /* sqrt(2) * (-c1-c3) */
z3 *= -FIX_1_961570560; /* sqrt(2) * (-c3-c5) */
z4 *= -FIX_0_390180644; /* sqrt(2) * (c5-c3) */
z3 += z5;
z4 += z5;
dataptr[56] = DESCALE(tmp4 + z1 + z3, CONST_BITS + PASS1_BITS);
dataptr[40] = DESCALE(tmp5 + z2 + z4, CONST_BITS + PASS1_BITS);
dataptr[24] = DESCALE(tmp6 + z2 + z3, CONST_BITS + PASS1_BITS);
dataptr[8] = DESCALE(tmp7 + z1 + z4, CONST_BITS + PASS1_BITS);
dataptr++; /* advance pointer to next column */
}
/* descale */
for (i = 0; i < 64; i++)
block[i] = (short int) DESCALE(data[i], 3);
}