Code implementation for fast inverse Discrete Cosine Transformation (fidct)

The following two-dimensional fast inverse Discrete Cosine transformation is based on the Code of Thomas G. Lane. It can be directly used for image or video processing.

The test code is written by xuanjicang Yishi.

// fidct.h

void fidct(short *const block);
void fidct_init();

// fidct.cpp

/*****************************************************************************
 *
 *  XVID MPEG-4 VIDEO CODEC
 *  - Inverse DCT  -
 *
 *  These routines are from Independent JPEG Group's free JPEG software
 *  Copyright (C) 1991-1998, Thomas G. Lane (see the file README.IJG)
 ****************************************************************************/

/* Copyright (C) 1996, MPEG Software Simulation Group. All Rights Reserved. */

#include "fidct.h"

#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) */

/* private data */
static short iclip[1024];  /* clipping table */
static short *iclp;

/* two dimensional inverse discrete cosine transform */
// fidct_init() MUST BE CALLED BEOFRE THE FIRST CALL TO THIS FUNCTION!
void fidct(short *const block)
{
 static short *blk;
 static long i;
 static long X0, X1, X2, X3, X4, X5, X6, X7, X8;

 for (i = 0; i < 8; i++)  /* idct rows */
 {
  blk = block + (i << 3);
  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;
   continue;
  }

  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] = (short) ((X7 + X1) >> 8);
  blk[1] = (short) ((X3 + X2) >> 8);
  blk[2] = (short) ((X0 + X4) >> 8);
  blk[3] = (short) ((X8 + X6) >> 8);
  blk[4] = (short) ((X8 - X6) >> 8);
  blk[5] = (short) ((X0 - X4) >> 8);
  blk[6] = (short) ((X3 - X2) >> 8);
  blk[7] = (short) ((X7 - X1) >> 8);

 }       /* end for ( i = 0; i < 8; ++i ) IDCT-rows */

 for (i = 0; i < 8; i++)  /* idct columns */
 {
  blk = block + i;
  /* shortcut  */
  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];
   continue;
  }

  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];
 }
} 

void fidct_init()
{
 int i;

 iclp = iclip + 512;
 for (i = -512; i < 512; i++)
  iclp[i] = (i < -256) ? -256 : ((i > 255) ? 255 : i);
}

// Test code: Calculate. cpp

#include <iostream>
#include "fidct.h"
using namespace std;

#define NUM 8

int main(void)
{
 int i, j;
 double originaldata[NUM][NUM] =
 {
  {1125.00, -32.00, -185.00, -7.00, 2.00, -1.00, -2.00, 2.00},
  {-22.00, -16.00, 45.00, -3.00, -2.00, 0.00, -1.00, -2.00},  
  {-165.00, 32.00, 17.00,  2.00,  1.00, -1.00, -3.00,  0.00},  
  {-7.00, -4.00,  0.00,  2.00,  2.00, -1.00, -1.00,  2.00},  
  {-2.00,  0.00,  0.00,  3.00,  0.00,  0.00,  2.00,  1.00},  
  {3.00,  1.00,  1.00, -1.00, -2.00,  1.00,  2.00,  0.00},  
  {0.00,  0.00,  2.00, -1.00, -1.00,  2.00,  1.00, -1.00},  
  {0.00,  3.00,  1.00, -1.00,  2.00,  1.00, -2.00,  0.00}  
 };

 short *data = new short[NUM * NUM];
 for(i = 0; i < NUM; i++)
 {
  for(j = 0; j < NUM; j++)
  {
   data[i * NUM + j] = (short)originaldata[i][j];
  }
 }
 fidct_init();
 fidct(data);
    for(i = 0; i < NUM; i++)
 {
  for(j = 0; j < NUM; j++)
  {
   cout << data[i * NUM + j] << '/t';
  }
  cout << endl;
 }
 return 0;
}

Running result:

  89   101   114   125   126   115   105     96 
   97   115   131   147   149   135   123   113 
114   134   159   178   175   164   149   137 
121   143   177   196   201   189   165   150 
119   141   175   201   207   186   162   144 
107   130   165   189   192   171   144   125 
  96   119   150   171   172   145   116      96 
  88   107   136   156   155   129      97     75

Please refer:

Code Implementation of Discrete Cosine regular inverse transformation and fast discrete cosine transformation (FDCT)