Embedded C for Digital Signal Processing - Signal Processing Systems - page 1246

#define N 16
X _Fract coeff[N] = { 0.7r, ... };

_Fract inner_product(Y _Fract * inp)
{

int i;
_Accum sum = 0.0k;
for (i = 0; i < N; i++)
{

sum += coeff[i] * (_Accum) * (inp++);

}
return (_Sat _Fract)sum;

}
The above example sums the products in an Accum typed variable sum .Itis
assumed that this summation will not overflow, because N is smaller or equal than
the integral part of the Accum . Only the final result is saturated back to a Fract .
The cast to Accum inside the loop makes sure that the multiplication is done
in the Accum type. Without this cast the multiplication would have been done in
Fract type and if both the coefficient and the input would have the exact value
− 0 which is out of range for a regular Fract ,

resulting in an overflow. In a normal FIR filter there will not however be a

1 . 0, then the result would be 1 .

0in
the coefficients. So in that case the Accum cast could be safely removed and the
multiplication would be performed within the Fract type.
The example also uses the memory spaces X and Y from where respectively the
inp and the coeff constants are retrieved. Assuming the target architecture looks
like the one described in Sect. 2 , every iteration of this loop could thus be performed
in one cycle.

− 1 .

5.2 Sine Function in Fixed Point

Another example of converting a floating point algorithm into fixed point is the
computation of the sine function.

#define F 5
static _Accum sinfract(_Accum x)
{

int f;
_Accum result = 1.0k;

for (f = 2 * F+1; f > 1; f -= 2)
{

result = 1.0k - result * x * x/(f * (f-1));

}