Although it’s not advertised, the Arduino / AVR compiler mostly does the right thing with long long = uint64_t variables: add & subtract work fine, but multiplication & division discard anything that doesn’t fit into 64 bits. Fitting a 32 bit integer and a 32 bit fraction into such a thing should eliminate (most) problems with significant figures.
The general idea is to set up a struct giving access to the two 32 bit halves for direct manipulation, then overlay / union them with a single 64 bit integer for arithmetic purposes:
struct ll_s {
uint32_t low;
uint32_t high;
};
union ll_u {
uint64_t ll_64;
struct ll_s ll_32;
};
Of course, the integer part still falls one bit shy of holding 2³². At the cost of one bit’s worth of resolution, you can still compute 2³² / 125×10⁶ by pre-dividing each quantity by 2:
2^63 = [80000000 00000000] 2^63 / 125/2 M = [00000022 5c17d04d]
The low-order digit should be 0xe, not 0xd, but I think that’s survivable.
Unfortunately, printf doesn’t handle 64 bit quantities, necessitating some awkward conversion routines. “Printing” to a string seems the least awful method, as I’ll eventually squirt the strings to a display, not send them to the serial port:
void PrintFractionLL(char *pBuffer,uint64_t *pLL) {
uint64_t Fraction;
Fraction = (uint32_t)*pLL; // copy 32 fraction bits, high order = 0
Fraction *= ONEGIG; // times 10^9 for conversion
Fraction >>= 32; // align integer part in low long
sprintf(pBuffer,"%09lu",(uint32_t)Fraction); // convert low long to decimal
}
void PrintIntegerLL(char *pBuffer,uint64_t *pLL) {
sprintf(pBuffer,"%lu",*((uint32_t *)pLL+1));
}
void PrintDecimalLL(char *pBuffer,uint64_t *pLL) {
PrintIntegerLL(pBuffer,pLL);
pBuffer += strlen(pBuffer); // pointer to end of integer part
*pBuffer++ = '.'; // drop in the decimal point, tick pointer
PrintFractionLL(pBuffer,pLL);
}
The result seems nearly indistinguishable from the Right Answer:
Integer: 34 Fraction: 359738367 Decimal: 34.359738367
This whole mess has a bunch of rough edges, but it looks promising. The code coalesced while fiddling around, so the union notation didn’t get much love at first.
The Arduino source code as a GitHub Gist:
