Binary counter: base 10 adjustment

Question

In a microcontroller (MSP430F5659) the RTCB timer provides clock-based interrupts at register-controlled intervals. These may be 1,2,4,8,16,32,64,128,256,512,1024 (and higher) interrupts per second. The same timer also provides a 1-second interrupt which is handy for evaluating the problem below.

Using one of the clock-based interrupts I'd like to update a variable called milliseconds. For reasons of efficiency and precision, I'm using the 1024 times per second interrupt.

Each interrupt represents 0.9765625 milliseconds. I don't want to store milliseconds as a float value, but rather as an integer.

I suppose incrementing a floating point variable by 0.9756525 and then rounding would do the trick, but I'd rather not add floating point processing overhead.

Therefore I need a mathematical function that will set my millisecond counter appropriately so it stays within +-1 ms. So, each time the interrupt fires, a decision is made whether or not the millisecond counter should be incremented (or wait until the next interrupt).

Answer 1

Let your master counter count interrupts rather than milliseconds. Then whenever someone needs a millisecond count, convert your interrupt count to milliseconds on the fly: $$ \mathit{millis} = \frac{1000}{1024}\mathit{intrs} = \mathit{intrs} - \frac{3\cdot \mathit{intrs}}{2^7} $$ where the division is just a bit shift.

Answer 2

You could have a second counter running and avoid incrementing the millisecond counter at 22, 65 and 107. At 128 this second counter should be reset to zero.