Are 32-bit floats sufficient for micros to RPM conversion?

README.md

Blog 2021/2/20

<- previous | index | next ->

Are 32-bit floats sufficient for microseconds-to-RPM conversion?

Answer: yes.

Engine ECU's calculate engine RPM by measuring the delay (in microseconds) between pulses from a crank position sensor.

Converting from micros to RPM can be performed as a single division (60 million / delay), but do 32-bit floats have sufficient resolution to produce usable results? We can write a simple C program to answer this.

Our expected range of values spans from cranking speed (about 240 RPM, or 250,000 micros) to engine redline (about 10,000 RPM, or 6,000 micros).

Output:

250000 micros -> 240.0000000000000000 rpm, (as bytes: 0x43700000)
250001 micros -> 239.9990386962890625 rpm, (as bytes: 0x436fffc1)
6000 micros -> 10000.0000000000000000 rpm, (as bytes: 0x461c4000)
6001 micros -> 9998.3339843750000000 rpm, (as bytes: 0x461c3956)

rpm.c

// Test of whether 32-bit floats are suitable for conversion from microseconds
// to revolutions per minute.

#include <stdint.h>
#include <stdio.h>

// gcc -std=c99 -O0 -Wall -Werror -o rpm rpm.c && ./rpm

int main() {
    // 250,000 micros represents cranking speed (240 RPM).
    // 6,000 micros represents redline (10,000 RPM).
    uint32_t nums[99] = {250000, 250001, 6000, 6001};
    for (int i=0; i < 4; i++) {
        uint32_t n = nums[i];
        float f = 60000000.0;
        float g = f / n;
        printf("%u micros -> %.16f rpm, (as bytes: 0x%x)\n", n, g, *(unsigned int*)&g);
    }
    return 0;
}

/* output:
250000 micros -> 240.0000000000000000 rpm, (as bytes: 0x43700000)
250001 micros -> 239.9990386962890625 rpm, (as bytes: 0x436fffc1)
6000 micros -> 10000.0000000000000000 rpm, (as bytes: 0x461c4000)
6001 micros -> 9998.3339843750000000 rpm, (as bytes: 0x461c3956)
*/