Looking for help in explaining two code lines

[alexBB]

I am facing a problem of converting the code below to Fortran. I've done such things before successfully but this one is a bit challenging. The code is taken from here:

http://www.holoborodko.com/pavel/numerical-methods/numerical-integration/

  double gauss_legendre(int n, double (*f)(double,void*), void* data, double a, double b)
{
	double* x = NULL;
	double* w = NULL;
	double A,B,Ax,s;
	int i, dtbl, m;

	m = (n+1)>>1;

	/* Load appropriate predefined table */
	dtbl = 0;
	for (i = 0; i<GLAWSIZE;i++)
	{
	  if(n==glaw[i].n)
	    {
	      x = glaw[i].x;
	      w = glaw[i].w;
	      break;
	    }
	}
	/* Generate new if non-predefined table is required */
	/* with precision of 1e-10 */
	if(NULL==x)
	{
	  dtbl = 1;
          x = (double*)malloc(m*sizeof(double));
	  w = (double*)malloc(m*sizeof(double));
          gauss_legendre_tbl(n,x,w,1e-10);
	}
	A = 0.5*(b-a);
	B = 0.5*(b+a);
	if(n&1) /* n - odd */
	{
	  s = w[0]*((*f)(B,data));    // <====
	  for (i=1;i<m;i++)
	  {
	    Ax = A*x[i];
            s += w[i]*((*f)(B+Ax,data)+(*f)(B-Ax,data));  // <====
	  }
	}
        else
        {                  /* n - even */
          s = 0.0;
	  for (i=0;i<m;i++)
	    {
	      Ax = A*x[i];
	      s += w[i]*((*f)(B+Ax,data)+(*f)(B-Ax,data));  // <====
	    }
	}
	if (dtbl)
	{
	  free(x);
	  free(w);
	}
	return A*s;
}

glaw is an outside array of this form:

static GLAW glaw[] = {							{2,x2,w2},
{3,x3,w3},
{4,x4,w4},
......... 

f is an outside (input) function (integrand). data is probably a work array.

I don't understand the statements I marked with leftward arrows. It looks like B+Ax, etc. is an argument. Why is data in there?

Also in the example.c file I found at the link, NULL is passed to the routine gauss_legendre, not an array.

Thanks, - Alex

[coder777]

Obviously the sole purpose of data is to be passed to f(...), in case the function requires more (only known outside gauss_legendre(...)) data to do it's job. The alternative to this parameter would be global variable. The creator of that function tried to avoid that.

Also in the example.c file I found at the link, NULL is passed to the routine gauss_legendre, not an array.

void * is completely generic, hence you can pass whatever (non const) you want.

[alexBB]

Thank you. It seems to have become clear now. - Alex