Calculate a third grade function with C on a STM32 microcontroller

Question

I'm trying to implement the following function to be calculated by my STM32

y=0.0006*x^3 - 0.054*x^2 + 2.9094*x - 2.3578

x is in range 0 to 215

To avoid the use of pow or any other functions, I have written the following code

static double tmp = 0;
static unsigned short c_m;
static unsigned short c_m_3;
static unsigned short c_m_2;

c_m_3 = c_m*c_m*c_m;
c_m_2 = c_m*c_m;
tmp = (0.0006*c_m_3) - (0.054*c_m_2) + (2.9094*c_m) - 2.3578;
dati->sch_g = tmp;

For some reason the calculation is totally wrong as, for istane, if c_m = 1 I should have tmp = 0.4982 instead I got 13

Am I missing something?

Answer 1

As denoted by Lundin in the comments your micro controller type (ARM Cortex M0) doesn't provide a floating point unit. This in consequence means you cannot rely on natural floating point math, but need to rely on a floating point software library like e.g. this one (note: I didn't evaluate, has just been the very first I stumbled upon on a quick search!).

Alternatively – and likely preferrably – you might want to do the calculations in plain integers; if you additionally convert your calculation from pattern a*x*x*x + b*x*x + c*x + d to ((a*x + b)*x + c)*x + d you even spare some mulitiplications:

int32_t c_m = ...;
c_m = ((6 * c_m - 540) * c_m + 29094) * c_m - 23578;

Note: unsigned short would be too small to hold the result on STM32, so you need to switch to 32 bit at least! Additionally you need a signed value to be able to hold the negative result arising from c_m == 0.

Your results would now be too large by a factor of 10 000, of course. As the use case is unclear question remains open how you would want to deal with, possibly rounding it (c_m = (c_m + 5000) / 10000) or evaluating the fractional part by other means.

Answer 2

short is 16 bits on all STM32. Thus the value 215 * 215 * 215 will not fit inside one. c_m_3 = c_m*c_m*c_m; truncates the result as per modulus USHRT_MAX+1 (65536):

Otherwise, if the new type is unsigned, the value is converted by repeatedly adding or subtracting one more than the maximum value that can be represented in the new type until the value is in the range of the new type.

Use uint32_t instead.

Answer 3

short is only 16 bits, the max value it can hold is 65535. Therefore it will overflow if the number you want to calculate the third power for is over 40. This means that you must use a larger variable type like uint32_t. You can also use ifs to detect overflow for better programming practices.

As another note, it's better to use "uint8_t" and "uint16_t" instead of "unsigned char" and "unsigned short" in embedded programming, because they're more descriptive of the data sizes.