Floating-point without FPU

Question

Since a Floating Point Unit (FPU) is not present in Arduino Uno, I wanted to know how float operations are performed. If it is simulated as integer operations, I want to know how exactly the simulation is done.

Answer 1

As I said in my comment, all float operations are implemented in software. As a simple test, I compiled the following program:

volatile float x, y, z;

int main(void)
{
    z = x + y;
    return 0;
}

The compiler translated the sum operation into a call to __addsf3. This function extends its arguments to flt40_t format (non-standard 40 bits float), calls __addsf3x to do the 40-bit addition, then calls __fp_round to convert the result into the standard float format. __addsf3x also makes a few library calls of its own. In the end, the addition pulled the following functions into the compiled program: __subsf3, __addsf3, __addsf3x, __fp_inf, __fp_nan, __fp_pscA, __fp_pscB, __fp_round, __fp_split3, __fp_splitA, __fp_zero and __fp_szero.

All these functions are provided by the avr-libc. You can find them in the libm/fplib directory. See for example the files:

• addsf3.S
• addsf3x.S
• fp_round.S

Answer 2

software emulation. The float is decomposed into sign, exponent and mantissa and then integer operations are used to do the actual math.

Addition and subtraction means shifting the mantissas to a common magnitude, adding/subtracting them and then checking the highest set bit for the new exponent.

Multiplication means adding the exponents and multiplying the mantissas. Division is subtracting.