Real to rational promotion

[mahrud]

Is this just the reality of how mpfr numbers work?

i1 : (1.2)_QQ

     5404319552844595
o1 = ----------------
     4503599627370496

o1 : QQ

i2 : (1.5)_QQ

     3
o2 = -
     2

o2 : QQ

[mahrud]

In other words, is there something subtly flawed about doing it naively?

i1 : f = r -> 1 + position(try precision r else defaultPrecision,
         e -> r * 10 - floor(r = r * 10) < 1e-15);

i2 : g = r -> (r * 10^(e := f(r)))_QQ / 10^e;

i3 : g(1.2)

     6
o3 = -
     5

o3 : QQ

i4 : g(12.3456)

     7716
o4 = ----
      625

o4 : QQ

i5 : g(pi)

     3141592653589793
o5 = ----------------
     1000000000000000

o5 : QQ

Probably the < 1e-15 part needs more thinking, is this the subtlety?

[d-torrance]

Techincally, RR objects are always going to be rational numbers whose denominators are a power of 2 since they're represented using binary. That's where the 4503599627370496 is coming from -- it's $2^{52}$. But I agree that 6/5 makes a lot more sense in this case.

I'm guessing instead of 1e-15, maybe it should be something like 10^(-floor(prec*log 2/log 10)) to account for precisions other than 53.

[mahrud]

So would it make sense to change something just so things like (1.2)_QQ look reasonable, or is it not a bad idea?

[d-torrance]

I think it makes sense.