Re: [boost] [multiprecision] Bug in double to cpp_bin_float conversion?

Subject: Re: [boost] [multiprecision] Bug in double to cpp_bin_float conversion?
From: M.A. van den Berg (thijs_at_[hidden])
Date: 2016-04-13 17:52:02

> On 13 Apr 2016, at 23:32, Rob Conde <rob.conde_at_[hidden]> wrote:
> 
> Consider the following code:
> 
> 
> #include <boost/multiprecision/cpp_bin_float.hpp>
> #include <iostream>
> 
> int main()
> {
>    typedef boost::multiprecision::cpp_bin_float_quad float128_t;
> 
>    float128_t f1(1e-9);
> 
>    float128_t f2("1e-9");
> 
>    std::cout << std::setprecision(std::numeric_limits<float128_t>::max_digits10);
> 
>    std::cout << f1 << std::endl;
>    std::cout << f2 << std::endl;
> 
>    return 0;
> }
> 
> 
> I'm getting as output:
> 
> 
> 1.000000000000000062281591457779856419e-09
> 9.999999999999999999999999999999999325e-10
> 
> The conversion of the double literal is not as expected.
> 
> On wand box: http://melpon.org/wandbox/permlink/uSGNQZAEEytmb3ao
> 
> 
> Is this a bug? If not, what would be the correct way to get my expected behavior?
> 
> 
> Thanks,
> 
> Rob Conde

This has to do with finite resolution of doubles, a double has roughly 16 significant, e.g. these next 3 numbers will all be converted to the same double (if truncated the last digits because it cant hold it)
0.99999999999999999-09
1.00000000000000000-09
1.00000000000000001-09

If you map a low resolution double to a higher resolution mil number then it’s just going to pad extra zeros at the end. The number you see might look weird, but in binary float notation it ends in a nice list of zeros.

http://www.binaryconvert.com/result_double.html?decimal=049101045057 <http://www.binaryconvert.com/result_double.html?decimal=049101045057>