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Best algorithm for calculating timer pre-scalar and period during run time?

Question asked by arnold_w on Jun 16, 2016
Latest reply on Jul 12, 2016 by arnold_w
I am working with the Discovery Development Board (STM32F407) and I would like to have functions for the 16-bit timers that looks like this:

void startTimer(uint32_t timeoutMs, EventCallback_t timerInterruptCallback)

I'm currently using the formula below, but I recently discovered and corrected an overflow problem that makes this algorithm pretty bad (the error is less than 1% for timeout values below 800 ms at 32 MHz timer clock, but above that it gets pretty bad). I don't want to use floating point mathematical operations or lookup tables. Does anyone have any clever ideas?

clockFreqBeforeDivision = GET_TIMER_FREQ(TIM2);
perfectClockFreqAfterDivision = (((uint32_t)(1000 * 65536)) / ((uint32_t)milliseconds));
divisor = 1 + (clockFreqBeforeDivision / perfectClockFreqAfterDivision);
actualClockFreqAfterDivision = clockFreqBeforeDivision / divisor;
timerPeriod = milliseconds * (actualClockFreqAfterDivision / 1000);