Issues with rounding in the GCC implementation of the ISO 18037:2008 standard fixed-point arithmetic

We describe various issues caused by the lack of rounding in the gcc compiler implementation of the fixed-point arithmetic data types and operations. We demonstrate that there is no rounding in the conversion of constants, conversion from one numerical type to a less precise type and results of multiplications. Furthermore, we show that mixed-precision operations of fixed-point arithmetic lose precision on arguments, even before carrying out arithmetic operations. The ISO 18037:2008 standard was created to standardize C language extensions, including fixed-point arithmetic, for embedded systems. Embedded systems are usually based on ARM processors, of which approximately 100 billion were manufactured by now. Therefore, the observations about numerical issues that we show in this paper can be rather dangerous and are important to address, given a wide ranging types of applications that these embedded systems are running.