You aren't guaranteed that your microcontrollers float is going to match your desktop. Microcontrollers are riddled with bugs, unless you need floats and fixedpoint is fast enough. My recommendation is still to use fixedpoint if application is high reliability.
Esp if your code needs to be portable across arm, risc-v, etc.
Fixed point isn't bad at all, just often slower when a compliant FPU is available.
IEEE only mandates results within ½ ULP (= best possible) for basic operations such as addition, subtraction, multiplication, division, and reciprocal.
For many other ones such as trigonometric functions, exponential and logarithms, results can (and do) vary between conforming implementations.
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.h...:
“The IEEE standard does not require transcendental functions to be exactly rounded because of the table maker's dilemma. To illustrate, suppose you are making a table of the exponential function to 4 places. Then exp(1.626) = 5.0835. Should this be rounded to 5.083 or 5.084? If exp(1.626) is computed more carefully, it becomes 5.08350. And then 5.083500. And then 5.0835000. Since exp is transcendental, this could go on arbitrarily long before distinguishing whether exp(1.626) is 5.083500...0ddd or 5.0834999...9ddd. Thus it is not practical to specify that the precision of transcendental functions be the same as if they were computed to infinite precision and then rounded. Another approach would be to specify transcendental functions algorithmically. But there does not appear to be a single algorithm that works well across all hardware architectures. Rational approximation, CORDIC,16 and large tables are three different techniques that are used for computing transcendentals on contemporary machines. Each is appropriate for a different class of hardware, and at present no single algorithm works acceptably over the wide range of current hardware.”
