# JPEG compression and DCT algorithm verification

Here is the code I am using to apply DCT on 8x8 blocks, which I'm not sure is correct. I have tried to follow Wikipedia's discrete cosine transformation (DCT) formula as closely as possible. Please let me know if there are any changes to be made.

//round up a float type and show two decimal places
double rndup(double n)
{
double t;
double temp;
t=n-floor(n);
if (t>=0.5)
{
n*=100.0;//where n is the multi-decimal float
n=ceil(n);
temp = floor(n);
temp = n - temp;
n-=temp;
n/=100.0;
}
else
{
n*=100.0;//where n is the multi-decimal float
n=floor(n);
temp = floor(n);
temp = n - temp;
n-=temp;
n/=100.0;
}
return n;
}
//two functions that work together to apply DCT to a 8x8 block
void a_check(int u,int v, double *Cu, double *Cv)
{
if (u == 0) *Cu = sqrt(1.0 / 8.0); else *Cu = sqrt(2.0 / 8.0);
if (v == 0) *Cv = sqrt(1.0 / 8.0); else *Cv = sqrt(2.0 / 8.0);
}
void applyDCT(double *DCTMatrix, double *Matrix,int x, int y)   //arguments: DCTMatrix = matrix where DCT values go, Matrix = input Matrix which needs to be processed
{
double Cu=0,Cv=0,cos_x=0,cos_y=0, DCT_value = 0;
for(int u=0;u<8;u++)
{
for(int v=0;v<8;v++)
{
a_check(u,v,&Cu,&Cv);
cos_x = cos( (3.14/8) * (double)u * ( (double) ( (x+u) + (1.0/2.0))));
cos_y = cos( (3.14/8) * (double)v * ( (double) ( (y+v) +(1.0/2.0))));
DCT_value = Cu * Cv * Matrix[u*8 + v] * cos_x * cos_y;
DCT_value = rndup(DCT_value);
DCTMatrix[u*8 + v] = DCT_value;
}
}
}

• It will be easier to answer your question if you include a link to the Wikipedia article you mentioned, and describe which formula from the article you are trying to implement Dec 1, 2012 at 23:02

I'll comment on readability as it could use some serious improvements.

• Your indentation is very inconsistent. Sometimes you indent two spaces, four spaces, eight spaces, or no spaces. Choose a style and keep it consistent throughout the program.

Two common styles (using four spaces):

void func()
{
if (isTrue)
{
// ...
}
}


void func() {
if (isTrue) {
// ...
}
}

• Your use of whitespace is also inconsistent. It'd be more readable to separate all operators and operands with one space and keep those consistent throughout the program.

Don't do this:

int number=1+2+3;


Do this:

int number = 1 + 2 + 3;

• This comment:

//where n is the multi-decimal float


can just be placed above the function. There's no need to put it in multiple places.

• The comment next to applyDCT() should probably be placed on top of the function instead. A comment that long should either be relocated or broken up into separate-lined comments.

• These:

if (u == 0) *Cu = sqrt(1.0 / 8.0); else *Cu = sqrt(2.0 / 8.0);
if (v == 0) *Cv = sqrt(1.0 / 8.0); else *Cv = sqrt(2.0 / 8.0);


are not very readable nor maintainable. Prefer to apply curly braces, especially if you'll need to add to any of the conditions:

if (u == 0)
{
*Cu = sqrt(1.0 / 8.0);
}
else
{
*Cu = sqrt(2.0 / 8.0);
}

// the same applies to the second aforementioned line

• Do not declare/initialize variables on the same line:

double Cu=0,Cv=0,cos_x=0,cos_y=0, DCT_value = 0;


double Cu = 0;