DSP Tech Brief : C Code To Implement The Q Format Number System

I recently posted an "Introduction To The Q Format Number System" : http://realgonegeek.blogspot.co.uk/2015/01/introduction-to-q-format-number-system.html.

This afternoon I was driving back from a meeting and thought I should put some code together to demonstrate the operations. Here it is (you will notice that I have used a somewhat more useful word length than 8 bits for this piece of code) :


#include <stdio.h>

double QFormatIntegerToFloat (const int x,
  const int n)

{
  return (((double)x) / ((double)(1 << n)));
}

int FloatToQFormatInteger (const double x,
  const int m,
  const int n)

{
  int   i;
  int   y;
  int   mask = 0;

  y = (int)(x * ((double)(1 << n)));  // Generate the integer number in m.n format

  for (i = 0; i < (m+n); i++)         // Calculate the mask to ensure we return the correct number of valid bits
  {
    mask = (mask << 1) + 1;
  }

  return (y & mask);
}

int MpyQFormatInteger (const int x,
  const int y,
  const int n)

{
  long long tmp;
  tmp = ((long long)x * (long long)y) >> n;
  return ((int)tmp);
}


int main() 
{
  int         a, b, c, d, e;


  printf ("%lf = 0x%x\n",  2.0 , FloatToQFormatInteger (2.0 , 8, 24));
  printf ("%lf = 0x%x\n",  1.5 , FloatToQFormatInteger (1.5 , 8, 24));
  printf ("%lf = 0x%x\n",  0.5 , FloatToQFormatInteger (0.5 , 8, 24));
  printf ("%lf = 0x%x\n",  0.25, FloatToQFormatInteger (0.25, 8, 24));
  printf ("%lf = 0x%x\n",  0.75, FloatToQFormatInteger (0.75, 8, 24));
  printf ("\n");

  a = FloatToQFormatInteger (0.75, 8, 24);
  b = FloatToQFormatInteger (2.0 , 8, 24);
  c = MpyQFormatInteger (a, b, 24);

  printf ("Result = 0x%x : %lf\n", c, QFormatIntegerToFloat (c , 24));

  d = FloatToQFormatInteger (0.5 , 8, 24);
  e = MpyQFormatInteger (c, d, 24);

  printf ("Result = 0x%x : %lf\n", e, QFormatIntegerToFloat (e , 24));

  return (0);
}

Here is the output :

2.000000 = 0x2000000
1.500000 = 0x1800000
0.500000 = 0x800000
0.250000 = 0x400000
0.750000 = 0xc00000

Result = 0x1800000 : 1.500000
Result = 0xc00000 : 0.750000

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