Following "idct" code is collected from MPEG reference code. "idct" means inverse
discrete cosine transform. It basically converts time-domain data to
frequency domain data like FFT(fast fourier transform). idct algorithm is
very popular in Multimedia, Mobile Communication, Image Processing and so on.
-----------------------------------------------------------------
/* idct.c, inverse fast discrete cosine transform */
#include <config.h>
#include <stdio.h>
#include "mjpeg_types.h"
#include "transfrm_ref.h"
/* Copyright (C) 1996, MPEG Software Simulation Group. All Rights Reserved. */
/*
* Disclaimer of Warranty
*
* These software programs are available to the user without any license fee or
* royalty on an "as is" basis. The MPEG Software Simulation Group disclaims
* any and all warranties, whether express, implied, or statuary, including any
* implied warranties or merchantability or of fitness for a particular
* purpose. In no event shall the copyright-holder be liable for any
* incidental, punitive, or consequential damages of any kind whatsoever
* arising from the use of these programs.
*
* This disclaimer of warranty extends to the user of these programs and user's
* customers, employees, agents, transferees, successors, and assigns.
*
* The MPEG Software Simulation Group does not represent or warrant that the
* programs furnished hereunder are free of infringement of any third-party
* patents.
*
* Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
* are subject to royalty fees to patent holders. Many of these patents are
* general enough such that they are unavoidable regardless of implementation
* design.
*
*/
/**********************************************************/
/* inverse two dimensional DCT, Chen-Wang algorithm */
/* (cf. IEEE ASSP-32, pp. 803-816, Aug. 1984) */
/* 32-bit integer arithmetic (8 bit coefficients) */
/* 11 mults, 29 adds per DCT */
/* sE, 18.8.91 */
/**********************************************************/
/* coefficients extended to 12 bit for IEEE1180-1990 */
/* compliance sE, 2.1.94 */
/**********************************************************/
/* this code assumes >> to be a two's-complement arithmetic */
/* right shift: (-2)>>1 == -1 , (-3)>>1 == -2 */
#define W1 2841 /* 2048*sqrt(2)*cos(1*pi/16) */
#define W2 2676 /* 2048*sqrt(2)*cos(2*pi/16) */
#define W3 2408 /* 2048*sqrt(2)*cos(3*pi/16) */
#define W5 1609 /* 2048*sqrt(2)*cos(5*pi/16) */
#define W6 1108 /* 2048*sqrt(2)*cos(6*pi/16) */
#define W7 565 /* 2048*sqrt(2)*cos(7*pi/16) */
/* global declarations */
/* private data */
static int16_t iclip[1024]; /* clipping table */
static int16_t *iclp;
/* private prototypes */
static void idctrow (int16_t *blk);
static void idctcol (int16_t *blk);
/* row (horizontal) IDCT
*
* 7 pi 1
* dst[k] = sum c[l] * src[l] * cos( -- * ( k + - ) * l )
* l=0 8 2
*
* where: c[0] = 128
* c[1..7] = 128*sqrt(2)
*/
static void idctrow(int16_t *blk)
{
int x0, x1, x2, x3, x4, x5, x6, x7, x8;
/* int16_tcut */
if (!((x1 = blk[4]<<11) | (x2 = blk[6]) | (x3 = blk[2]) |
(x4 = blk[1]) | (x5 = blk[7]) | (x6 = blk[5]) | (x7 = blk[3])))
{
blk[0]=blk[1]=blk[2]=blk[3]=blk[4]=blk[5]=blk[6]=blk[7]=blk[0]<<3;
return;
}
x0 = (blk[0]<<11) + 128; /* for proper rounding in the fourth stage */
/* first stage */
x8 = W7*(x4+x5);
x4 = x8 + (W1-W7)*x4;
x5 = x8 - (W1+W7)*x5;
x8 = W3*(x6+x7);
x6 = x8 - (W3-W5)*x6;
x7 = x8 - (W3+W5)*x7;
/* second stage */
x8 = x0 + x1;
x0 -= x1;
x1 = W6*(x3+x2);
x2 = x1 - (W2+W6)*x2;
x3 = x1 + (W2-W6)*x3;
x1 = x4 + x6;
x4 -= x6;
x6 = x5 + x7;
x5 -= x7;
/* third stage */
x7 = x8 + x3;
x8 -= x3;
x3 = x0 + x2;
x0 -= x2;
x2 = (181*(x4+x5)+128)>>8;
x4 = (181*(x4-x5)+128)>>8;
/* fourth stage */
blk[0] = (x7+x1)>>8;
blk[1] = (x3+x2)>>8;
blk[2] = (x0+x4)>>8;
blk[3] = (x8+x6)>>8;
blk[4] = (x8-x6)>>8;
blk[5] = (x0-x4)>>8;
blk[6] = (x3-x2)>>8;
blk[7] = (x7-x1)>>8;
}
/* column (vertical) IDCT
*
* 7 pi 1
* dst[8*k] = sum c[l] * src[8*l] * cos( -- * ( k + - ) * l )
* l=0 8 2
*
* where: c[0] = 1/1024
* c[1..7] = (1/1024)*sqrt(2)
*/
static void idctcol(int16_t *blk)
{
int x0, x1, x2, x3, x4, x5, x6, x7, x8;
/* int16_tcut */
if (!((x1 = (blk[8*4]<<8)) | (x2 = blk[8*6]) | (x3 = blk[8*2]) |
(x4 = blk[8*1]) | (x5 = blk[8*7]) | (x6 = blk[8*5]) | (x7 = blk[8*3])))
{
blk[8*0]=blk[8*1]=blk[8*2]=blk[8*3]=blk[8*4]=blk[8*5]=blk[8*6]=blk[8*7]=
iclp[(blk[8*0]+32)>>6];
return;
}
x0 = (blk[8*0]<<8) + 8192;
/* first stage */
x8 = W7*(x4+x5) + 4;
x4 = (x8+(W1-W7)*x4)>>3;
x5 = (x8-(W1+W7)*x5)>>3;
x8 = W3*(x6+x7) + 4;
x6 = (x8-(W3-W5)*x6)>>3;
x7 = (x8-(W3+W5)*x7)>>3;
/* second stage */
x8 = x0 + x1;
x0 -= x1;
x1 = W6*(x3+x2) + 4;
x2 = (x1-(W2+W6)*x2)>>3;
x3 = (x1+(W2-W6)*x3)>>3;
x1 = x4 + x6;
x4 -= x6;
x6 = x5 + x7;
x5 -= x7;
/* third stage */
x7 = x8 + x3;
x8 -= x3;
x3 = x0 + x2;
x0 -= x2;
x2 = (181*(x4+x5)+128)>>8;
x4 = (181*(x4-x5)+128)>>8;
/* fourth stage */
blk[8*0] = iclp[(x7+x1)>>14];
blk[8*1] = iclp[(x3+x2)>>14];
blk[8*2] = iclp[(x0+x4)>>14];
blk[8*3] = iclp[(x8+x6)>>14];
blk[8*4] = iclp[(x8-x6)>>14];
blk[8*5] = iclp[(x0-x4)>>14];
blk[8*6] = iclp[(x3-x2)>>14];
blk[8*7] = iclp[(x7-x1)>>14];
}
/* two dimensional inverse discrete cosine transform */
void idct(int16_t *block)
{
int i;
for (i=0; i<8; i++)
idctrow(block+8*i);
for (i=0; i<8; i++)
idctcol(block+i);
}
void init_idct(void)
{
int i;
iclp = iclip+512;
for (i= -512; i<512; i++)
iclp[i] = (i<-256) ? -256 : ((i>255) ? 255 : i);
}
