[prog] c types confusion

[Daniel.]

>You have 8*sizeof(float) bits to work with
>(on my computer that would be 32)

(Maybe this was the missing piece of information that led dominik to 
wonder why you would assume float would lose precision before 2^31; 
sizeof(float) is 8 on some machines.)

>Those 32 bits now have to be split between the base (I
>don't think that's quite the right word) and the
>exponent (mantissa?).

That's correct.

>So if you have: 2.456e14 then you'd have x bits to
>store the 2456 and y bits to store the 14 and you are
>constrained by x + y = 32.
>
>Now, 2^32 = 4294967296 = 4.294967296e9, and its going
>to take all your 32 bits to store the: 4.294967296,
>leaving nothing to store the: 9, so won't it get
>approximated to: 4.294967e9, or something?

The base and exponent are stored in binary, so when you lose 
precision, the base gets rounded to a round binary number, i.e. a 
multiple of a power of 2. But you happen to be storing powers of two 
in it anyway, which means it happens to come out exact. Try storing 
2^32-1 in there; it won't work.
-Daniel.
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