Precise floating-point<->string conversion
<p>I am looking for a library function to convert floating point numbers to strings, and back again, in C++. The properties I want are that str2num(num2str(x)) == x and that num2str(str2num(x)) == x (as far as possible). The general property is that num2str should represent the simplest rational number that when rounded to the nearest representable floating pointer number gives you back the original number.</p>

<p>So far I've tried boost::lexical_cast:</p>

<pre><code>double d = 1.34;
string_t s = boost::lexical_cast&lt;string_t&gt;(d);
printf("%s\n", s.c_str());
// outputs 1.3400000000000001
</code></pre>

<p>And I've tried std::ostringstream, which seems to work for most values if I do stream.precision(16). However, at precision 15 or 17 it either truncates or gives ugly output for things like 1.34. I don't think that precision 16 is guaranteed to have any particular properties I require, and suspect it breaks down for many numbers.</p>

<p>Is there a C++ library that has such a conversion? Or is such a conversion function already buried somewhere in the standard libraries/boost.</p>

<p>The reason for wanting these functions is to save floating point values to CSV files, and then read them correctly. In addition, I'd like the CSV files to contain simple numbers as far as possible so they can be consumed by humans.</p>

<p>I know that the Haskell read/show functions already have the properties I am after, as do the BSD C libraries. The standard references for string&lt;->double conversions is a pair of papers from PLDI 1990:</p>

<ul>
<li>How to read floating point numbers accurately, Will Klinger</li>
<li>How to print floating point numbers accurately, Guy Steele et al</li>
</ul>

<p>Any C++ library/function based on these would be suitable.</p>

<p>EDIT: I am fully aware that floating point numbers are inexact representations of decimal numbers, and that 1.34==1.3400000000000001. However, as the papers referenced above point out, that's no excuse for choosing to display as "1.3400000000000001"</p>

<p>EDIT2: This paper explains exactly what I'm looking for: <a href="http://drj11.wordpress.com/2007/07/03/python-poor-printing-of-floating-point/" rel="nofollow">http://drj11.wordpress.com/2007/07/03/python-poor-printing-of-floating-point/</a></p>
