Appendix A: A C Program for the Fast Discrete Cosine Transform

 /*ffdct.c*/ /*fast forward discrete cosine transform in the current   frame */ #include "config.h" #include "global.h" #define W1 2841        /* sqrt(2)cos(π/16)<< 11*/ #define W2 2676        /* sqrt(2)cos(2π/16)<< 11*/ #define W3 2408        /* sqrt(2)cos(3π/16)<< 11*/ #define W5 1609        /* sqrt(2)cos(5π/16)<< 11*/ #define W6 1108        /* sqrt(2)cos(6π/16)<< 11*/ #define W7 565         /* sqrt(2)cos(7π/16)<< 11*/ #define W10 2276       /* W1 - W7 */ #define W11 3406       /* W1 + W7 */ #define W12 4017       /* W3 + W5 */ #define W13 799        /* W3 - W5 */ #define W14 1568       /* W2 - W6 */ #define W15 3784       /* W2 + W6 */ /* global declarations */ void ffdct _ANSI_ARGS_((int *block)); void ffdct(block) int *block; { int s [10] ,t [10] ,r [10] ; int *p; int j, temp; /*forward transformation in "H" direction*/ p = block; for(j=0; j<64; j +=8 )    {    /* first stage transformation */    s[0] = (*(p) + *(p+7));    s[1] = (*(p+1) + *(p+6));    s[2] = (*(p+2) + *(p+5));    s[3] = (*(p+3) + *(p+4));    s[4] = (*(p+3) - *(p+4));    s[5] = (*(p+2) - *(p+5));    s[6] = (*(p+1) - *(p+6));    s[7] = (*(p)   - *(p+7));    /* second stage transformation */    t[0] = s[0] + s[3];    t[1] = s[1] + s[2] ;    t[2] = s[1] - s[2] ;    t[3] = s[0] - s[3] ;    t[5] = ((s[6] - s[5]) * 181) >> 8;    t[6] = ((s[6] + s[5]) * 181) >> 8;    /* third stage transformation */    r[4] = s[4] + t[5];    r[5] = s[4] - t[5];    r[6] = s[7] - t[6];    r[7] = s[7] + t[6];    /* fourth stage transformation */    block[0+j] = (t[0] + t[1]);    block[4+j] = (t[0] - t[1]);    temp = (r[4] + r[7]) * W1;    block[1+j] = (temp - r[4] * W10) >> 11;    block[7+j] = (r[7] * W11 - temp) >> 11;    temp = ( r[5] + r[6]) * W3 ;    block[3+j] = (temp - r[5] * W12) >> 11;    block[5+j] = (temp - r[6] * W13) >> 11;    temp = (t[2] + t[3]) * W6;    block[2+j] = (temp + t[3] * W14) >> 11;    block[6+j] = (temp - t[2] * W15) >> 11;    P += 8;    } /* forward transformation in 'V' direction */ for(j=0; j<8; j++)    {    /* first stage transformation */    s[0] = block[j] + block[j+56];    s[1] = block[j+8] + block[j+48];    s[2] = block[j+16] + block[j+40];    s[3] = block[j+24] + block[j+32];    s[4] = block[j+24] - block[j+32];    s[5] = block[j+16] - block[j+40];    s[6] = block[j+8] - block[j+48];    s[7] = block[j] - block [j+56];    /* second stage transformation */    t[0] = s[0] + s[3];    t[1] = s[l] + s[2];    t[2] = s[l] - s[2];    t[3] = s[0] - s[3];    t[5] = ((s[6] - s[5]) * 181) >> 8;    t[6] = ((s[6] + s[5]) * 181) >> 8;    /* third stage transformation */    r[4] = s[4] + t[5];    r[5] = s[4] - t[5];    r[6] = s[7] - t[6];    r[7] = s[7] + t[6];    /* fourth stage transformation */    /* transform coefficients */    /* coefficients are divided by 8 and rounded */    block[0+j]= ((t[0] + t[l]) + 4) >> 3;    block[32+j]= ((t[0] - t[1]) + 4) >> 3;    temp = (r[4] + r[7]) * W1;    block[8+j]= ((temp - r[4] * W10) + 8192) >> 14;    block[56+j]= (((r[7] * W11) - temp) + 8192) >> 14;    temp = (r[5] + r[6]) * W3 ;    block[24+j]= ((temp - r[5] * W12) + 8192) >> 14;    block[40+j]= ((temp - r[6] * W13) + 8192) >> 14;    temp = (t[2] + t[3]) * W6;    block[16+j]= ((temp + t[3] * W14) + 8192) >> 14;    block[48+j]= ((temp - t[2] * W15) + 8192) >> 14;    } }