Re: [Boost-bugs] [Boost C++ Libraries] #12327: cpp_rational::convert_to<double>() does not return the nearest number

Subject: Re: [Boost-bugs] [Boost C++ Libraries] #12327: cpp_rational::convert_to<double>() does not return the nearest number
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2016-07-15 04:46:21

#12327: cpp_rational::convert_to<double>() does not return the nearest number
-------------------------------+----------------------------
  Reporter:  komakisen@…       |      Owner:  johnmaddock
      Type:  Bugs              |     Status:  new
 Milestone:  To Be Determined  |  Component:  multiprecision
   Version:  Boost 1.61.0      |   Severity:  Problem
Resolution:                    |   Keywords:
-------------------------------+----------------------------

Comment (by komakisen@…):

 Replying to [comment:1 johnmaddock]:

 > Then r112 becomes 5404319552844595/54043195528445952 which is
 0.0999999999999999962992565845828115319212277730305989583... in decimal,
 which rounds up to 0.10000000000000001 and not down to
 0.099999999999999992 due to the "6" after the string of 9's.

 Thank you for investigating my program, but I still don't understand this
 point.

 To begin with, 0.099999999999999992 is actually
 0.09999999999999999167332... and 0.10000000000000001 is actually
 0.1000000000000000055511... (they differ by 1ulp)

 So 0.09999999999999999629925... is less than their midpoint
 0.09999999999999999861222...

 Also, `double` is a binary floating-point number. Thus I believe round-off
 calculation on a decimal digit "6" explains nothing here.

 If I run the following program, I get 0.099999999999999992.

 {{{#!c++
 #include <iostream>
 #include <iomanip>
 using namespace std;

 int main() {
    double d = 0.09999999999999999629926;
    std::cout << std::setprecision(17) << d << std::endl;
    return 0;
 }
 }}}

 So isn't 0.099999999999999992 the expected result? Or am I confusing
 myself?

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/12327#comment:2>
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