Re: float to string to float, with first float == second float

Pete Becker <>
Tue, 06 Oct 2009 11:06:45 -0400
Rune Allnor wrote:

On 6 Okt, 15:04, Victor Bazarov <> wrote:

Rune Allnor wrote:

On 6 Okt, 14:22, Nick Keighley <>

On 6 Oct, 12:39, Rune Allnor <> wrote:

On 6 Okt, 11:16, Carsten Fuchs <> wrote:

I would like to serialize a float f1 to a string s, then unserialize s back to a float f2
again, such that:
        * s is minimal (use only the precision that is required)
          and preferably in decimal notation,
        * f1==f2 (exact same value after the roundtrip)
(The first property is for human readers and file size, the second is for data integrity.)

You should choose between *either* human readability *or*
data integrity. You can't have both.
To demonstrate the point, try
#include <iostream>
int main()
        float a=0.3;
        double b = a;
        std::cout << "a = " << a << std::endl;
        std::cout << "b = " << b << std::endl;
        return 0;}
a = 0.3
b = 0.300000011921
There are two problems here:
1) Numbers that are exact in decimal notation
   have no exact floating-point representation,
   only an approximation.

try 0.5

Or 0.25, 0.125, 0.0625, etc., or *any combination thereof*. Then factor
in the exponents.


That's one of the few

*Few*? You're kidding, of course, aren't you?

No. There are infinitely many real numbers between
any two consecutive FP numbers.

That's a different issue. The question was how to write out values that
are represented in floating-point so that you can read them back in exactly.

 Using the IEEE
definition of "single precision float", there are *about* (2^32 - 2^24)
decimal values that can be represented *exactly*. Each of all the other
values (infinite number of them, of course) are rounded to one of the
*more than three billion* representations (my arithmetic may be off a tad).

Three billions is still a finite number of representations.
True, it is large enough to be useful, but still finite.

But there are only a finite number of floating-point values, so being
finite is not, in itself, a limitation.

 > decimal numbers that can be represented

exactly on binary format. In fact, decimal numbers on the form
x = 2^n
where n is selected from a certain subset of integers, can be
represented exactly, as binary numbers. If the OP can accept
such a constraint on the decimal numbers he wants to work with,
then by all means, disregard what I said. But if he wants to
work with arbitrary numbers, he is in for trouble.

No, he is not "in for trouble". He just needs to realise that computer
representation of the floating point numbers have limitations, and *stay
within those limitations*.

As I understand the question, the OP wants to break out
of those limitations: Exact conversions between base-10
and base-2 numbers, eliminating approximation errors etc.

No, he's looking for conversions of the finite set of values that can be
represented as floating-point.

Roundhouse Consulting, Ltd. ( Author of
"The Standard C++ Library Extensions: a Tutorial and Reference"

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