Question

I have a situation which requires a float to be represented in a single char. The range that this ‘minifloat’ needs to represent is 0 to 10e-7, so we can always assume that the number is +ve, and the exponent -ve in order to save space.

The representation that I have thought about going with is 3 bits of exponent, and 5 bits mantissa (with 1 implied bit), with the exponent being in base 10, i.e. x = man * 10^exp.

To convert from a float to my minifloat, I plan to use frexp, and use some maths to convert from base 2 to base 10.

Is this a sensible approach? Or are there better ways to achieve this?

Answer 1

Do you actually need the value to be floating point (i.e. to have roughly constant precision as the value scales)? What are you going to do with these values?

A much simpler (and more efficient) idea would be to interpret 8 bits as an unsigned fixed-point number with an implicit scale of 1e-7. I.e.:

float toFloat(uint8_t x) {
    return x / 255.0e7;
}

uint8_t fromFloat(float x) {
    if (x < 0) return 0;
    if (x > 1e-7) return 255;
    return 255.0e7 * x; // this truncates; add 0.5 to round instead
}