Floating Point¶
This is not strictly D specific, but since “95% of the folks out there are completely clueless about floating-point” (James Gosling, Keynote 1998), it might be a good idea to talk about IEEE 754. There is an excellent article by Don Clugston on the D website, which goes into the details of D floating point stuff. For this tutorial, I give you a few guidelines from Kahan (page 43) applied to D:
- All Rules of Thumb but this one are fallible. Good reasons to break rules arise occasionally.
- Store data and results no more precisely than you need and trust. Is float enough? In doubt, use double.
- Local or temporary variables should be highly precise. In doubt, use real.
- Field types should be parsimonious (float?). Computed properties should be precise (double or real?).
Rule 0 applies to all content in this tutorial, but for sake of completeness, it is listed here explicitly. Rule 3 actually sounds like a corollary of rule 1 and 2 to me.
Differences to C¶
If you are coming from C/C++, then you are (hopefully) aware of the difference between the following two functions.
double a(double x, double y) {
return y + (x - y);
}
double b(double x, double y) {
double tmp = x-y;
return y + tmp;
}
The difference is that hardware might compute the x-y expression with higher precision than double (e.g. 80bit on x86). In the case of b, the compiler must round the tmp expression to double precision before the addition, but not in a. This can result in different return values. However, in D semantics those two versions are equivalent. Hence the guideline from above to use real tmp.
Also, D might evaluate such functions at compile time with yet another precision than the hardware.