How to manually convert between fixed type and floating type?

I am using a library which has fixed point variables.The library is called libfixmath.

I am trying to see how a number gets converted from a fix16_t to a float type. I understand it uses 32 bits (16 MSB bits for integers and 16 LSB bits for decimals) to represent a number.

This is the code I tried, here "sum" is of type fix16_t.

float in_sum = fix16_to_float(sum);
printf("fix16 type sum:%u\n",sum);
printf("float type sum:%f\n",in_sum);

I display the "sum" in an unsigned integer format, again I'm not sure the best format to display the "sum" value.

A sample output I got is:

fix16 type sum:4064807395
float type sum:-3511.961426

I had a look at the conversion function:

static inline float   fix16_to_float(fix16_t a) { return (float)a / fix16_one; }

Where fix16_one is 65536.

To get a better understanding I want to be able to convert this manually, but I do not know how. I am confused with the type casting (float)a.

Another question I have is, are the 16 integer bits signed or unsigned?

Solution

If fix16_t is an integer type, then a / 65536 would be an integer division, without any decimals. For example 65535 / 65536 is not the floating point value 0.99998, but the integer value 0.

The casting of a converts a and therefore the whole expression into a floating point division, with decimals.

Using the values:

Integer division: -230159901 / 65536 will result in the integer value -3511.
Floating point division: (float)-230159901 / 65536 will result in the float value -3511.961426.