Re: float to string to float, with first float == second float
Rune Allnor wrote:
On 6 Okt, 15:47, Carsten Fuchs <CarstenFu...@T-Online.de> wrote:
Rune Allnor wrote:
1) Approximations might occur when the value is first loaded
2) Approximations might occur when the value is serialized
3) Approximations might occur when the value is de-serialized
The problem is steps 2) and 3): Unless you can guarantee
that either
a) No approximations occur in steps 2) and 3)
b) The approximation in 3) exactly cancels the
approximation introduced in 2)
Yes, agreed, one or both of a) and b is/are the implied assumption.
I also should have mentioned in my original post where I got the idea for all this from:http://www.open-std.org/JTC1/sc22/wg21/docs/papers/2006/n2005.pdf
So if I understand this correctly, for step 2) there is a certain number of digits (max_digits10 in
the paper) that express the original value in "equal or higher precision" than was in the original
float.
OK, so let's play with numbers:
The number D of digits needed to represent a number N in
base 10 notation is
D = ceil(log10(N)).
For a single-precision floating-point number, there are some
20 bits in the mantissa, so the number of digits D to represent
the mantissa becomes
D = ceil(log10(2^20))
= ceil(20*log10(2))
> 20*floor(log10(2))
> 20*3
log10(2) == 0.3
> 60.
Should be 6
So one needs *at*least* 60 digits to represent the number.
Six, actually. Check your math.
Of course, a similar argument is used for the exponent.
[..snip..]
V
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