simple template metaprogramming example

[Paulo Herrera]

I've been experimenting with D's template capabilities to speed up some  
number crunching codes.
In that process I adapted the evaluation of the dot product of two arrays,  
originally in C++ and found at:  
http://osl.iu.edu/~tveldhui/papers/techniques/.

I think the D version is very concise and simple to understand, so it  
could be added to the examples given in the templates documentation. On  
the other hand, this kind of examples could motivate people working on  
numerical codes to try D.

--------------------------------------------
/// Rational:
///  Using a loop to compute the dot product of two small/medium size  
float arrays, e.g.
///
///     float s = 0.0;
///     for (int i=0, i < size, ++i)
///           s += a[i]*b[i];
///     return s;
///
///  can be very inefficient when compared to the hand written expression
///
///     return a[O]*b[0] + a[1]*b[1] + .....;
///
///  Using template metaprogramming we can get the same effect without  
explicitly writing
///  code for different array size and type.

struct dot_product(T, int N) {
     static T opCall (T[N] a, T[N] b) {
         return meta_dot!(N-1, N, T)(a,b); // expands to: a[0]*b[0]  
+ a[1]*b[1] + .... at compilation time
     }
}

struct meta_dot(int I, int N, T) {
     static T opCall(T[N] a, T[N] b) {
         static if (I == 0)
    	    return a[0]*b[0];
         else
    	    return a[I]*b[I] + meta_dot!(I-1, N, T)(a,b);
      }
}

// -------
// Usage:
// -------
float[3] a;
float[3] b;
a[] = 0.5;
b[] = 0.5;
float dot = dot_product!(float, 3)(a, b);
writefln("dot: %f", dot); // = 0.750000
---------------------------------------------

Paulo